86=5x^2-34

Solution for 86=5x^2-34 equation:

86=5x^2-34

We move all terms to the left:

86-(5x^2-34)=0

We get rid of parentheses

-5x^2+34+86=0

We add all the numbers together, and all the variables

-5x^2+120=0

a = -5; b = 0; c = +120;
Δ = b2-4ac
Δ = 02-4·(-5)·120
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*-5}=\frac{0-20\sqrt{6}}{-10}
=-\frac{20\sqrt{6}}{-10}
=-\frac{2\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*-5}=\frac{0+20\sqrt{6}}{-10}
=\frac{20\sqrt{6}}{-10}
=\frac{2\sqrt{6}}{-1}
$