52+180x2=26+90

Solution for 52+180x2=26+90 equation:

52+180x^2=26+90

We move all terms to the left:

52+180x^2-(26+90)=0

We add all the numbers together, and all the variables

180x^2+52-116=0

We add all the numbers together, and all the variables

180x^2-64=0

a = 180; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·180·(-64)
Δ = 46080
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:

$\sqrt{\Delta}=\sqrt{46080}=\sqrt{9216*5}=\sqrt{9216}*\sqrt{5}=96\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{5}}{2*180}=\frac{0-96\sqrt{5}}{360}
=-\frac{96\sqrt{5}}{360}
=-\frac{4\sqrt{5}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{5}}{2*180}=\frac{0+96\sqrt{5}}{360}
=\frac{96\sqrt{5}}{360}
=\frac{4\sqrt{5}}{15}
$