Use equation method to solve problems

Use the formula method to solve the following equations

1. Solution: 2X²-4X-1=0

Here a=2,b=-4,c=-1

b^ 2-4ac=(-4)^ 2-4*2*(-1)=24

x=[-(-4)±√24]/(2*2)=(2±√6)/2

So x=(2 √6)/2 or x=(2-√6)/2

2. Solution: 5X 2=3X² (Personally, I think the cross multiplication method should be faster)

3X²-5x-2=0

Here a=3,b=-5,c=-2

b^ 2-4ac=(-5)^ 2-4*3*(-2)=49

x=[-(-5)±√49]/(2*3)=(5±7)/6

So x=2 or x=-1/3

3. Solution: (X-2) (3X-5)=1

3x^ 2-11x 9=0

Here a=3,b=-11,c=9

b^ 2-4ac=(-11) ^ 2-4*3*9=13

x=[-(-11)±√13]/(2*3)=(6±√13)/6

So x=(6 √13)/6 or x=(6-√13)/6

9th grade math! Solve equations using formula method

p(p-8)=16

p²-8p-16=0

a=1, b=-8, c=-16

p1=[-b √（b²-4ac)]/(2a)=[-(-8) √（（-8）²-4*1*(-16))]/(2*1) =8/2=4

p2=[-b-√（b²-4ac）]/(2a)=[-(-8)-√（（-8）²-4*1*(-16))]/(2* 1)=8/2=4

x² x-12=0

a=1, b=1, c=-12

x1=[-b √（b²-4ac）]/(2a)=[-1 √（1²-4*1*(-12))]/(2*1)=(-1 √49) /2=3

x2=[-b-√（b²-4ac）]/(2a)=[-1-√（1²-4*1*(-12))]/(2*1)=(-1- √49)/2=-4

2x² 5x-3=0

a=2, b=5, c=-3

x1=[-b √（b²-4ac)]/(2a)=[-5 √（5²-4*2*(-3))]/(2*2)=(-5 √49) /4=1/2

x2=[-b-√（b²-4ac）]/(2a)=[-5-√（5²-4*2*(-3))]/(2*2)=(-5- √49)/4=-3

6x²-13x-5=0

a=6, b=-13, c=-5

x1=[-b √（b²-4ac）]/(2a)=[-(-13) √（（-13）²-4*6*(-5))]/(2*6) =(13 √289)/12=5/2

x2=[-b-√（b²-4ac）]/(2a)=[-(-13)-√（（-13）²-4*6*(-5))]/(2* 6)=(13-√289)/12=-1/3

What is the formula method for solving quadratic equations in mathematics

An integral equation that contains only one unknown number (one variable) and the highest degree of the unknown term is 2 (quadratic) is called a quadratic equation of one variable. Standard form: ax² bx c=0(a≠0). Where ax² is a quadratic term, a is a quadratic term coefficient; b is a linear term coefficient; bx is a linear term; c is a constant term.

There are 5 solutions to quadratic equations of one variable, namely the direct square root method, the combination method, the formula method, the factorization method, and the cross multiplication method.

The value of the unknown that makes the left and right sides of the quadratic equation equal is the solution to the quadratic equation. The solution of a quadratic equation is also called the root of a quadratic equation (the solution of an equation containing only one unknown is also called the root of this equation).

The roots of a quadratic equation and the discriminant of the roots have the following relationship: Δ=b^2-4ac

Suppose ax² bx c=0(a≠0) in the quadratic equation of one variable. The two roots x₁ and x₂ have the following relationship:

x₁ x₂=-b/a;x₁*x₂=c/a

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