(2x-5)(x+5)=180

Solution for (2x-5)(x+5)=180 equation:

(2x-5)(x+5)=180

We move all terms to the left:

(2x-5)(x+5)-(180)=0

We multiply parentheses ..

(+2x^2+10x-5x-25)-180=0

We get rid of parentheses

2x^2+10x-5x-25-180=0

We add all the numbers together, and all the variables

2x^2+5x-205=0

a = 2; b = 5; c = -205;
Δ = b2-4ac
Δ = 52-4·2·(-205)
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{185}}{2*2}=\frac{-5-3\sqrt{185}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{185}}{2*2}=\frac{-5+3\sqrt{185}}{4}
$