81x^2+180x-100=0

Solution for 81x^2+180x-100=0 equation:

81x^2+180x-100=0

a = 81; b = 180; c = -100;
Δ = b2-4ac
Δ = 1802-4·81·(-100)
Δ = 64800
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:

$\sqrt{\Delta}=\sqrt{64800}=\sqrt{32400*2}=\sqrt{32400}*\sqrt{2}=180\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180\sqrt{2}}{2*81}=\frac{-180-180\sqrt{2}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180\sqrt{2}}{2*81}=\frac{-180+180\sqrt{2}}{162}
$