81x^2-12x-16=0

Solution for 81x^2-12x-16=0 equation:

81x^2-12x-16=0

a = 81; b = -12; c = -16;
Δ = b2-4ac
Δ = -122-4·81·(-16)
Δ = 5328
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:

$\sqrt{\Delta}=\sqrt{5328}=\sqrt{144*37}=\sqrt{144}*\sqrt{37}=12\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{37}}{2*81}=\frac{12-12\sqrt{37}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{37}}{2*81}=\frac{12+12\sqrt{37}}{162}
$