12x^2-108x+160=0

Solution for 12x^2-108x+160=0 equation:

12x^2-108x+160=0

a = 12; b = -108; c = +160;
Δ = b2-4ac
Δ = -1082-4·12·160
Δ = 3984
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:

$\sqrt{\Delta}=\sqrt{3984}=\sqrt{16*249}=\sqrt{16}*\sqrt{249}=4\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{249}}{2*12}=\frac{108-4\sqrt{249}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{249}}{2*12}=\frac{108+4\sqrt{249}}{24}
$