8x^2-9=82

Solution for 8x^2-9=82 equation:

8x^2-9=82

We move all terms to the left:

8x^2-9-(82)=0

We add all the numbers together, and all the variables

8x^2-91=0

a = 8; b = 0; c = -91;
Δ = b2-4ac
Δ = 02-4·8·(-91)
Δ = 2912
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:

$\sqrt{\Delta}=\sqrt{2912}=\sqrt{16*182}=\sqrt{16}*\sqrt{182}=4\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{182}}{2*8}=\frac{0-4\sqrt{182}}{16}
=-\frac{4\sqrt{182}}{16}
=-\frac{\sqrt{182}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{182}}{2*8}=\frac{0+4\sqrt{182}}{16}
=\frac{4\sqrt{182}}{16}
=\frac{\sqrt{182}}{4}
$