53=8+9x^2

Solution for 53=8+9x^2 equation:

53=8+9x^2

We move all terms to the left:

53-(8+9x^2)=0

We get rid of parentheses

-9x^2-8+53=0

We add all the numbers together, and all the variables

-9x^2+45=0

a = -9; b = 0; c = +45;
Δ = b2-4ac
Δ = 02-4·(-9)·45
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{5}}{2*-9}=\frac{0-18\sqrt{5}}{-18}
=-\frac{18\sqrt{5}}{-18}
=-\frac{\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{5}}{2*-9}=\frac{0+18\sqrt{5}}{-18}
=\frac{18\sqrt{5}}{-18}
=\frac{\sqrt{5}}{-1}
$