13x^2-152=0

Solution for 13x^2-152=0 equation:

13x^2-152=0

a = 13; b = 0; c = -152;
Δ = b2-4ac
Δ = 02-4·13·(-152)
Δ = 7904
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:

$\sqrt{\Delta}=\sqrt{7904}=\sqrt{16*494}=\sqrt{16}*\sqrt{494}=4\sqrt{494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{494}}{2*13}=\frac{0-4\sqrt{494}}{26}
=-\frac{4\sqrt{494}}{26}
=-\frac{2\sqrt{494}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{494}}{2*13}=\frac{0+4\sqrt{494}}{26}
=\frac{4\sqrt{494}}{26}
=\frac{2\sqrt{494}}{13}
$