45=5x^2+10

Solution for 45=5x^2+10 equation:

45=5x^2+10

We move all terms to the left:

45-(5x^2+10)=0

We get rid of parentheses

-5x^2-10+45=0

We add all the numbers together, and all the variables

-5x^2+35=0

a = -5; b = 0; c = +35;
Δ = b2-4ac
Δ = 02-4·(-5)·35
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{7}}{2*-5}=\frac{0-10\sqrt{7}}{-10}
=-\frac{10\sqrt{7}}{-10}
=-\frac{\sqrt{7}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{7}}{2*-5}=\frac{0+10\sqrt{7}}{-10}
=\frac{10\sqrt{7}}{-10}
=\frac{\sqrt{7}}{-1}
$