13x^2-7=62

Solution for 13x^2-7=62 equation:

13x^2-7=62

We move all terms to the left:

13x^2-7-(62)=0

We add all the numbers together, and all the variables

13x^2-69=0

a = 13; b = 0; c = -69;
Δ = b2-4ac
Δ = 02-4·13·(-69)
Δ = 3588
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:

$\sqrt{\Delta}=\sqrt{3588}=\sqrt{4*897}=\sqrt{4}*\sqrt{897}=2\sqrt{897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{897}}{2*13}=\frac{0-2\sqrt{897}}{26}
=-\frac{2\sqrt{897}}{26}
=-\frac{\sqrt{897}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{897}}{2*13}=\frac{0+2\sqrt{897}}{26}
=\frac{2\sqrt{897}}{26}
=\frac{\sqrt{897}}{13}
$