56x^2-84x+31=0

Solution for 56x^2-84x+31=0 equation:

56x^2-84x+31=0

a = 56; b = -84; c = +31;
Δ = b2-4ac
Δ = -842-4·56·31
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{7}}{2*56}=\frac{84-4\sqrt{7}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{7}}{2*56}=\frac{84+4\sqrt{7}}{112}
$