81x^2+4x-12=0

Solution for 81x^2+4x-12=0 equation:

81x^2+4x-12=0

a = 81; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·81·(-12)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{61}}{2*81}=\frac{-4-8\sqrt{61}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{61}}{2*81}=\frac{-4+8\sqrt{61}}{162}
$