(10x+20)(10x-20)=180

Solution for (10x+20)(10x-20)=180 equation:

(10x+20)(10x-20)=180

We move all terms to the left:

(10x+20)(10x-20)-(180)=0

We use the square of the difference formula

100x^2-400-180=0

We add all the numbers together, and all the variables

100x^2-580=0

a = 100; b = 0; c = -580;
Δ = b2-4ac
Δ = 02-4·100·(-580)
Δ = 232000
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:

$\sqrt{\Delta}=\sqrt{232000}=\sqrt{1600*145}=\sqrt{1600}*\sqrt{145}=40\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{145}}{2*100}=\frac{0-40\sqrt{145}}{200}
=-\frac{40\sqrt{145}}{200}
=-\frac{\sqrt{145}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{145}}{2*100}=\frac{0+40\sqrt{145}}{200}
=\frac{40\sqrt{145}}{200}
=\frac{\sqrt{145}}{5}
$