3x2-5=81

Solution for 3x2-5=81 equation:

3x^2-5=81

We move all terms to the left:

3x^2-5-(81)=0

We add all the numbers together, and all the variables

3x^2-86=0

a = 3; b = 0; c = -86;
Δ = b2-4ac
Δ = 02-4·3·(-86)
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{258}}{2*3}=\frac{0-2\sqrt{258}}{6}
=-\frac{2\sqrt{258}}{6}
=-\frac{\sqrt{258}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{258}}{2*3}=\frac{0+2\sqrt{258}}{6}
=\frac{2\sqrt{258}}{6}
=\frac{\sqrt{258}}{3}
$