(3x+20)(-2x+55)=90

Solution for (3x+20)(-2x+55)=90 equation:

(3x+20)(-2x+55)=90

We move all terms to the left:

(3x+20)(-2x+55)-(90)=0

We multiply parentheses ..

(-6x^2+165x-40x+1100)-90=0

We get rid of parentheses

-6x^2+165x-40x+1100-90=0

We add all the numbers together, and all the variables

-6x^2+125x+1010=0

a = -6; b = 125; c = +1010;
Δ = b2-4ac
Δ = 1252-4·(-6)·1010
Δ = 39865
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{-(125)-\sqrt{39865}}{2*-6}=\frac{-125-\sqrt{39865}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+\sqrt{39865}}{2*-6}=\frac{-125+\sqrt{39865}}{-12}
$