(x+10)(x+50)=180

Solution for (x+10)(x+50)=180 equation:

(x+10)(x+50)=180

We move all terms to the left:

(x+10)(x+50)-(180)=0

We multiply parentheses ..

(+x^2+50x+10x+500)-180=0

We get rid of parentheses

x^2+50x+10x+500-180=0

We add all the numbers together, and all the variables

x^2+60x+320=0

a = 1; b = 60; c = +320;
Δ = b2-4ac
Δ = 602-4·1·320
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{145}}{2*1}=\frac{-60-4\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{145}}{2*1}=\frac{-60+4\sqrt{145}}{2}
$