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