13x^2-91=13

Solution for 13x^2-91=13 equation:

13x^2-91=13

We move all terms to the left:

13x^2-91-(13)=0

We add all the numbers together, and all the variables

13x^2-104=0

a = 13; b = 0; c = -104;
Δ = b2-4ac
Δ = 02-4·13·(-104)
Δ = 5408
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:

$\sqrt{\Delta}=\sqrt{5408}=\sqrt{2704*2}=\sqrt{2704}*\sqrt{2}=52\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52\sqrt{2}}{2*13}=\frac{0-52\sqrt{2}}{26}
=-\frac{52\sqrt{2}}{26}
=-2\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52\sqrt{2}}{2*13}=\frac{0+52\sqrt{2}}{26}
=\frac{52\sqrt{2}}{26}
=2\sqrt{2}
$