8x^2+5=76

Solution for 8x^2+5=76 equation:

8x^2+5=76

We move all terms to the left:

8x^2+5-(76)=0

We add all the numbers together, and all the variables

8x^2-71=0

a = 8; b = 0; c = -71;
Δ = b2-4ac
Δ = 02-4·8·(-71)
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{142}}{2*8}=\frac{0-4\sqrt{142}}{16}
=-\frac{4\sqrt{142}}{16}
=-\frac{\sqrt{142}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{142}}{2*8}=\frac{0+4\sqrt{142}}{16}
=\frac{4\sqrt{142}}{16}
=\frac{\sqrt{142}}{4}
$