81x^2+18x-5=0

Solution for 81x^2+18x-5=0 equation:

81x^2+18x-5=0

a = 81; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·81·(-5)
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{6}}{2*81}=\frac{-18-18\sqrt{6}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{6}}{2*81}=\frac{-18+18\sqrt{6}}{162}
$