78x^2+160x-100=0

Solution for 78x^2+160x-100=0 equation:

78x^2+160x-100=0

a = 78; b = 160; c = -100;
Δ = b2-4ac
Δ = 1602-4·78·(-100)
Δ = 56800
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:

$\sqrt{\Delta}=\sqrt{56800}=\sqrt{400*142}=\sqrt{400}*\sqrt{142}=20\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-20\sqrt{142}}{2*78}=\frac{-160-20\sqrt{142}}{156}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+20\sqrt{142}}{2*78}=\frac{-160+20\sqrt{142}}{156}
$