12x2-56x+40=0

Solution for 12x2-56x+40=0 equation:

12x^2-56x+40=0

a = 12; b = -56; c = +40;
Δ = b2-4ac
Δ = -562-4·12·40
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{-(-56)-8\sqrt{19}}{2*12}=\frac{56-8\sqrt{19}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{19}}{2*12}=\frac{56+8\sqrt{19}}{24}
$