6x2+128x+56=0

Solution for 6x2+128x+56=0 equation:

6x^2+128x+56=0

a = 6; b = 128; c = +56;
Δ = b2-4ac
Δ = 1282-4·6·56
Δ = 15040
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:

$\sqrt{\Delta}=\sqrt{15040}=\sqrt{64*235}=\sqrt{64}*\sqrt{235}=8\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-8\sqrt{235}}{2*6}=\frac{-128-8\sqrt{235}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+8\sqrt{235}}{2*6}=\frac{-128+8\sqrt{235}}{12}
$