9x^2-8=53

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

9x^2-8=53

We move all terms to the left:

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

We add all the numbers together, and all the variables

9x^2-61=0

a = 9; b = 0; c = -61;
Δ = b2-4ac
Δ = 02-4·9·(-61)
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{61}}{2*9}=\frac{0-6\sqrt{61}}{18}
=-\frac{6\sqrt{61}}{18}
=-\frac{\sqrt{61}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{61}}{2*9}=\frac{0+6\sqrt{61}}{18}
=\frac{6\sqrt{61}}{18}
=\frac{\sqrt{61}}{3}
$