(2x+8)(71-x)=90

Solution for (2x+8)(71-x)=90 equation:

(2x+8)(71-x)=90

We move all terms to the left:

(2x+8)(71-x)-(90)=0

We add all the numbers together, and all the variables

(2x+8)(-1x+71)-90=0

We multiply parentheses ..

(-2x^2+142x-8x+568)-90=0

We get rid of parentheses

-2x^2+142x-8x+568-90=0

We add all the numbers together, and all the variables

-2x^2+134x+478=0

a = -2; b = 134; c = +478;
Δ = b2-4ac
Δ = 1342-4·(-2)·478
Δ = 21780
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:

$\sqrt{\Delta}=\sqrt{21780}=\sqrt{4356*5}=\sqrt{4356}*\sqrt{5}=66\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(134)-66\sqrt{5}}{2*-2}=\frac{-134-66\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(134)+66\sqrt{5}}{2*-2}=\frac{-134+66\sqrt{5}}{-4}
$