4x(x+9)=(3x-2)(x+9)

Solution for 4x(x+9)=(3x-2)(x+9) equation:

4x(x+9)=(3x-2)(x+9)

We move all terms to the left:

4x(x+9)-((3x-2)(x+9))=0

We multiply parentheses

4x^2+36x-((3x-2)(x+9))=0

We multiply parentheses ..

4x^2-((+3x^2+27x-2x-18))+36x=0


We calculate terms in parentheses: -((+3x^2+27x-2x-18)), so:

(+3x^2+27x-2x-18)

We get rid of parentheses

3x^2+27x-2x-18

We add all the numbers together, and all the variables

3x^2+25x-18

Back to the equation:

-(3x^2+25x-18)


We add all the numbers together, and all the variables

4x^2+36x-(3x^2+25x-18)=0

We get rid of parentheses

4x^2-3x^2+36x-25x+18=0

We add all the numbers together, and all the variables

x^2+11x+18=0

a = 1; b = 11; c = +18;
Δ = b2-4ac
Δ = 112-4·1·18
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*1}=\frac{-4}{2}
=-2
$