5x2-82=250

Solution for 5x2-82=250 equation:

5x^2-82=250

We move all terms to the left:

5x^2-82-(250)=0

We add all the numbers together, and all the variables

5x^2-332=0

a = 5; b = 0; c = -332;
Δ = b2-4ac
Δ = 02-4·5·(-332)
Δ = 6640
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:

$\sqrt{\Delta}=\sqrt{6640}=\sqrt{16*415}=\sqrt{16}*\sqrt{415}=4\sqrt{415}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{415}}{2*5}=\frac{0-4\sqrt{415}}{10}
=-\frac{4\sqrt{415}}{10}
=-\frac{2\sqrt{415}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{415}}{2*5}=\frac{0+4\sqrt{415}}{10}
=\frac{4\sqrt{415}}{10}
=\frac{2\sqrt{415}}{5}
$