40+13x+x^2=108

Solution for 40+13x+x^2=108 equation:

40+13x+x^2=108

We move all terms to the left:

40+13x+x^2-(108)=0

We add all the numbers together, and all the variables

x^2+13x-68=0

a = 1; b = 13; c = -68;
Δ = b2-4ac
Δ = 132-4·1·(-68)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-21}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+21}{2*1}=\frac{8}{2}
=4
$