36x^2-92=53

Solution for 36x^2-92=53 equation:

36x^2-92=53

We move all terms to the left:

36x^2-92-(53)=0

We add all the numbers together, and all the variables

36x^2-145=0

a = 36; b = 0; c = -145;
Δ = b2-4ac
Δ = 02-4·36·(-145)
Δ = 20880
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:

$\sqrt{\Delta}=\sqrt{20880}=\sqrt{144*145}=\sqrt{144}*\sqrt{145}=12\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{145}}{2*36}=\frac{0-12\sqrt{145}}{72}
=-\frac{12\sqrt{145}}{72}
=-\frac{\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{145}}{2*36}=\frac{0+12\sqrt{145}}{72}
=\frac{12\sqrt{145}}{72}
=\frac{\sqrt{145}}{6}
$