(6x-40)(-3x+180)=x+20

Solution for (6x-40)(-3x+180)=x+20 equation:

(6x-40)(-3x+180)=x+20

We move all terms to the left:

(6x-40)(-3x+180)-(x+20)=0

We get rid of parentheses

(6x-40)(-3x+180)-x-20=0

We multiply parentheses ..

(-18x^2+1080x+120x-7200)-x-20=0

We add all the numbers together, and all the variables

(-18x^2+1080x+120x-7200)-1x-20=0

We get rid of parentheses

-18x^2+1080x+120x-1x-7200-20=0

We add all the numbers together, and all the variables

-18x^2+1199x-7220=0

a = -18; b = 1199; c = -7220;
Δ = b2-4ac
Δ = 11992-4·(-18)·(-7220)
Δ = 917761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1199)-\sqrt{917761}}{2*-18}=\frac{-1199-\sqrt{917761}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1199)+\sqrt{917761}}{2*-18}=\frac{-1199+\sqrt{917761}}{-36}
$