4x(x-3)+2x(x-2)=9x2-12x+4-8

Solution for 4x(x-3)+2x(x-2)=9x2-12x+4-8 equation:

4x(x-3)+2x(x-2)=9x^2-12x+4-8

We move all terms to the left:

4x(x-3)+2x(x-2)-(9x^2-12x+4-8)=0

We multiply parentheses

4x^2+2x^2-12x-4x-(9x^2-12x+4-8)=0

We get rid of parentheses

4x^2+2x^2-9x^2-12x-4x+12x-4+8=0

We add all the numbers together, and all the variables

-3x^2-4x+4=0

a = -3; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-3)·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-3}=\frac{-4}{-6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-3}=\frac{12}{-6}
=-2
$