-2x(x-12)-5(x+2)=-9x+4x

Solution for -2x(x-12)-5(x+2)=-9x+4x equation:

-2x(x-12)-5(x+2)=-9x+4x

We move all terms to the left:

-2x(x-12)-5(x+2)-(-9x+4x)=0

We add all the numbers together, and all the variables

-2x(x-12)-5(x+2)-(-5x)=0

We multiply parentheses

-2x^2+24x-5x-(-5x)-10=0

We get rid of parentheses

-2x^2+24x-5x+5x-10=0

We add all the numbers together, and all the variables

-2x^2+24x-10=0

a = -2; b = 24; c = -10;
Δ = b2-4ac
Δ = 242-4·(-2)·(-10)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{31}}{2*-2}=\frac{-24-4\sqrt{31}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{31}}{2*-2}=\frac{-24+4\sqrt{31}}{-4}
$