60-64x+12x^2=0

Solution for 60-64x+12x^2=0 equation:

60-64x+12x^2=0

a = 12; b = -64; c = +60;
Δ = b2-4ac
Δ = -642-4·12·60
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{19}}{2*12}=\frac{64-8\sqrt{19}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{19}}{2*12}=\frac{64+8\sqrt{19}}{24}
$