5=2x^2-10

Solution for 5=2x^2-10 equation:

5=2x^2-10

We move all terms to the left:

5-(2x^2-10)=0

We get rid of parentheses

-2x^2+10+5=0

We add all the numbers together, and all the variables

-2x^2+15=0

a = -2; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-2)·15
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-2}=\frac{0-2\sqrt{30}}{-4}
=-\frac{2\sqrt{30}}{-4}
=-\frac{\sqrt{30}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-2}=\frac{0+2\sqrt{30}}{-4}
=\frac{2\sqrt{30}}{-4}
=\frac{\sqrt{30}}{-2}
$