-56x^2+174x-115=0

Solution for -56x^2+174x-115=0 equation:

-56x^2+174x-115=0

a = -56; b = 174; c = -115;
Δ = b2-4ac
Δ = 1742-4·(-56)·(-115)
Δ = 4516
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:

$\sqrt{\Delta}=\sqrt{4516}=\sqrt{4*1129}=\sqrt{4}*\sqrt{1129}=2\sqrt{1129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(174)-2\sqrt{1129}}{2*-56}=\frac{-174-2\sqrt{1129}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(174)+2\sqrt{1129}}{2*-56}=\frac{-174+2\sqrt{1129}}{-112}
$