20n^2-88n+12=0

Solution for 20n^2-88n+12=0 equation:

20n^2-88n+12=0

a = 20; b = -88; c = +12;
Δ = b2-4ac
Δ = -882-4·20·12
Δ = 6784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6784}=\sqrt{64*106}=\sqrt{64}*\sqrt{106}=8\sqrt{106}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-8\sqrt{106}}{2*20}=\frac{88-8\sqrt{106}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+8\sqrt{106}}{2*20}=\frac{88+8\sqrt{106}}{40}
$