(x+14)(x+13)=15

Solution for (x+14)(x+13)=15 equation:

(x+14)(x+13)=15

We move all terms to the left:

(x+14)(x+13)-(15)=0

We multiply parentheses ..

(+x^2+13x+14x+182)-15=0

We get rid of parentheses

x^2+13x+14x+182-15=0

We add all the numbers together, and all the variables

x^2+27x+167=0

a = 1; b = 27; c = +167;
Δ = b2-4ac
Δ = 272-4·1·167
Δ = 61
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{-(27)-\sqrt{61}}{2*1}=\frac{-27-\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{61}}{2*1}=\frac{-27+\sqrt{61}}{2}
$