(2x+55)(x-15)=180

Solution for (2x+55)(x-15)=180 equation:

(2x+55)(x-15)=180

We move all terms to the left:

(2x+55)(x-15)-(180)=0

We multiply parentheses ..

(+2x^2-30x+55x-825)-180=0

We get rid of parentheses

2x^2-30x+55x-825-180=0

We add all the numbers together, and all the variables

2x^2+25x-1005=0

a = 2; b = 25; c = -1005;
Δ = b2-4ac
Δ = 252-4·2·(-1005)
Δ = 8665
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{-(25)-\sqrt{8665}}{2*2}=\frac{-25-\sqrt{8665}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{8665}}{2*2}=\frac{-25+\sqrt{8665}}{4}
$