12x^2-104x+165=0

Solution for 12x^2-104x+165=0 equation:

12x^2-104x+165=0

a = 12; b = -104; c = +165;
Δ = b2-4ac
Δ = -1042-4·12·165
Δ = 2896
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:

$\sqrt{\Delta}=\sqrt{2896}=\sqrt{16*181}=\sqrt{16}*\sqrt{181}=4\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{181}}{2*12}=\frac{104-4\sqrt{181}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{181}}{2*12}=\frac{104+4\sqrt{181}}{24}
$