(-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^2-205x+1010=0

a = 6; b = -205; c = +1010;
Δ = b2-4ac
Δ = -2052-4·6·1010
Δ = 17785
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{-(-205)-\sqrt{17785}}{2*6}=\frac{205-\sqrt{17785}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-205)+\sqrt{17785}}{2*6}=\frac{205+\sqrt{17785}}{12}
$