(x+16)(x+13)=270

Solution for (x+16)(x+13)=270 equation:

(x+16)(x+13)=270

We move all terms to the left:

(x+16)(x+13)-(270)=0

We multiply parentheses ..

(+x^2+13x+16x+208)-270=0

We get rid of parentheses

x^2+13x+16x+208-270=0

We add all the numbers together, and all the variables

x^2+29x-62=0

a = 1; b = 29; c = -62;
Δ = b2-4ac
Δ = 292-4·1·(-62)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-33}{2*1}=\frac{-62}{2}
=-31
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+33}{2*1}=\frac{4}{2}
=2
$