13x^2=24

Solution for 13x^2=24 equation:

13x^2=24

We move all terms to the left:

13x^2-(24)=0

a = 13; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·13·(-24)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{78}}{2*13}=\frac{0-4\sqrt{78}}{26}
=-\frac{4\sqrt{78}}{26}
=-\frac{2\sqrt{78}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{78}}{2*13}=\frac{0+4\sqrt{78}}{26}
=\frac{4\sqrt{78}}{26}
=\frac{2\sqrt{78}}{13}
$