(x+6)(x+10)=180

Solution for (x+6)(x+10)=180 equation:

(x+6)(x+10)=180

We move all terms to the left:

(x+6)(x+10)-(180)=0

We multiply parentheses ..

(+x^2+10x+6x+60)-180=0

We get rid of parentheses

x^2+10x+6x+60-180=0

We add all the numbers together, and all the variables

x^2+16x-120=0

a = 1; b = 16; c = -120;
Δ = b2-4ac
Δ = 162-4·1·(-120)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{46}}{2*1}=\frac{-16-4\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{46}}{2*1}=\frac{-16+4\sqrt{46}}{2}
$