x*(x+14)=108

Solution for x*(x+14)=108 equation:

x(x+14)=108

We move all terms to the left:

x(x+14)-(108)=0

We multiply parentheses

x^2+14x-108=0

a = 1; b = 14; c = -108;
Δ = b2-4ac
Δ = 142-4·1·(-108)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{157}}{2*1}=\frac{-14-2\sqrt{157}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{157}}{2*1}=\frac{-14+2\sqrt{157}}{2}
$