(2x+20)(2x+40)=1064

Solution for (2x+20)(2x+40)=1064 equation:

(2x+20)(2x+40)=1064

We move all terms to the left:

(2x+20)(2x+40)-(1064)=0

We multiply parentheses ..

(+4x^2+80x+40x+800)-1064=0

We get rid of parentheses

4x^2+80x+40x+800-1064=0

We add all the numbers together, and all the variables

4x^2+120x-264=0

a = 4; b = 120; c = -264;
Δ = b2-4ac
Δ = 1202-4·4·(-264)
Δ = 18624
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:

$\sqrt{\Delta}=\sqrt{18624}=\sqrt{64*291}=\sqrt{64}*\sqrt{291}=8\sqrt{291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-8\sqrt{291}}{2*4}=\frac{-120-8\sqrt{291}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+8\sqrt{291}}{2*4}=\frac{-120+8\sqrt{291}}{8}
$