X(x-11)=14

Solution for X(x-11)=14 equation:

X(X-11)=14

We move all terms to the left:

X(X-11)-(14)=0

We multiply parentheses

X^2-11X-14=0

a = 1; b = -11; c = -14;
Δ = b2-4ac
Δ = -112-4·1·(-14)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{177}}{2*1}=\frac{11-\sqrt{177}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{177}}{2*1}=\frac{11+\sqrt{177}}{2}
$