52x^2=752

Solution for 52x^2=752 equation:

52x^2=752

We move all terms to the left:

52x^2-(752)=0

a = 52; b = 0; c = -752;
Δ = b2-4ac
Δ = 02-4·52·(-752)
Δ = 156416
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:

$\sqrt{\Delta}=\sqrt{156416}=\sqrt{256*611}=\sqrt{256}*\sqrt{611}=16\sqrt{611}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{611}}{2*52}=\frac{0-16\sqrt{611}}{104}
=-\frac{16\sqrt{611}}{104}
=-\frac{2\sqrt{611}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{611}}{2*52}=\frac{0+16\sqrt{611}}{104}
=\frac{16\sqrt{611}}{104}
=\frac{2\sqrt{611}}{13}
$