X(x+11)=312

Solution for X(x+11)=312 equation:

X(X+11)=312

We move all terms to the left:

X(X+11)-(312)=0

We multiply parentheses

X^2+11X-312=0

a = 1; b = 11; c = -312;
Δ = b2-4ac
Δ = 112-4·1·(-312)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-37}{2*1}=\frac{-48}{2}
=-24
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+37}{2*1}=\frac{26}{2}
=13
$