5x^2-80=5+3x^2

Solution for 5x^2-80=5+3x^2 equation:

5x^2-80=5+3x^2

We move all terms to the left:

5x^2-80-(5+3x^2)=0

We get rid of parentheses

5x^2-3x^2-5-80=0

We add all the numbers together, and all the variables

2x^2-85=0

a = 2; b = 0; c = -85;
Δ = b2-4ac
Δ = 02-4·2·(-85)
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{170}}{2*2}=\frac{0-2\sqrt{170}}{4}
=-\frac{2\sqrt{170}}{4}
=-\frac{\sqrt{170}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{170}}{2*2}=\frac{0+2\sqrt{170}}{4}
=\frac{2\sqrt{170}}{4}
=\frac{\sqrt{170}}{2}
$