7x^2-56x+108=0

Solution for 7x^2-56x+108=0 equation:

7x^2-56x+108=0

a = 7; b = -56; c = +108;
Δ = b2-4ac
Δ = -562-4·7·108
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{-(-56)-4\sqrt{7}}{2*7}=\frac{56-4\sqrt{7}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{7}}{2*7}=\frac{56+4\sqrt{7}}{14}
$