13x=2x^2+13

Solution for 13x=2x^2+13 equation:

13x=2x^2+13

We move all terms to the left:

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

We get rid of parentheses

-2x^2+13x-13=0

a = -2; b = 13; c = -13;
Δ = b2-4ac
Δ = 132-4·(-2)·(-13)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{65}}{2*-2}=\frac{-13-\sqrt{65}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{65}}{2*-2}=\frac{-13+\sqrt{65}}{-4}
$