13x^2-169=0

Solution for 13x^2-169=0 equation:

13x^2-169=0

a = 13; b = 0; c = -169;
Δ = b2-4ac
Δ = 02-4·13·(-169)
Δ = 8788
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:

$\sqrt{\Delta}=\sqrt{8788}=\sqrt{676*13}=\sqrt{676}*\sqrt{13}=26\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{13}}{2*13}=\frac{0-26\sqrt{13}}{26}
=-\frac{26\sqrt{13}}{26}
=-\sqrt{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{13}}{2*13}=\frac{0+26\sqrt{13}}{26}
=\frac{26\sqrt{13}}{26}
=\sqrt{13}
$