x(x+14)=312

Solution for x(x+14)=312 equation:

x(x+14)=312

We move all terms to the left:

x(x+14)-(312)=0

We multiply parentheses

x^2+14x-312=0

a = 1; b = 14; c = -312;
Δ = b2-4ac
Δ = 142-4·1·(-312)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-38}{2*1}=\frac{-52}{2}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+38}{2*1}=\frac{24}{2}
=12
$