12x(x-11)=15

Solution for 12x(x-11)=15 equation:

12x(x-11)=15

We move all terms to the left:

12x(x-11)-(15)=0

We multiply parentheses

12x^2-132x-15=0

a = 12; b = -132; c = -15;
Δ = b2-4ac
Δ = -1322-4·12·(-15)
Δ = 18144
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:

$\sqrt{\Delta}=\sqrt{18144}=\sqrt{1296*14}=\sqrt{1296}*\sqrt{14}=36\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-36\sqrt{14}}{2*12}=\frac{132-36\sqrt{14}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+36\sqrt{14}}{2*12}=\frac{132+36\sqrt{14}}{24}
$