(10x+24)-x(6x+72)=180

Solution for (10x+24)-x(6x+72)=180 equation:

(10x+24)-x(6x+72)=180

We move all terms to the left:

(10x+24)-x(6x+72)-(180)=0

We multiply parentheses

-6x^2+(10x+24)-72x-180=0

We get rid of parentheses

-6x^2+10x-72x+24-180=0

We add all the numbers together, and all the variables

-6x^2-62x-156=0

a = -6; b = -62; c = -156;
Δ = b2-4ac
Δ = -622-4·(-6)·(-156)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-10}{2*-6}=\frac{52}{-12}
=-4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+10}{2*-6}=\frac{72}{-12}
=-6
$