(3x-5)(x+55)=180

Solution for (3x-5)(x+55)=180 equation:

(3x-5)(x+55)=180

We move all terms to the left:

(3x-5)(x+55)-(180)=0

We multiply parentheses ..

(+3x^2+165x-5x-275)-180=0

We get rid of parentheses

3x^2+165x-5x-275-180=0

We add all the numbers together, and all the variables

3x^2+160x-455=0

a = 3; b = 160; c = -455;
Δ = b2-4ac
Δ = 1602-4·3·(-455)
Δ = 31060
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:

$\sqrt{\Delta}=\sqrt{31060}=\sqrt{4*7765}=\sqrt{4}*\sqrt{7765}=2\sqrt{7765}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-2\sqrt{7765}}{2*3}=\frac{-160-2\sqrt{7765}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+2\sqrt{7765}}{2*3}=\frac{-160+2\sqrt{7765}}{6}
$