-x2+13=3x

Solution for -x2+13=3x equation:

-x2+13=3x

We move all terms to the left:

-x2+13-(3x)=0

We add all the numbers together, and all the variables

-1x^2-3x+13=0

a = -1; b = -3; c = +13;
Δ = b2-4ac
Δ = -32-4·(-1)·13
Δ = 61
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{-(-3)-\sqrt{61}}{2*-1}=\frac{3-\sqrt{61}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{61}}{2*-1}=\frac{3+\sqrt{61}}{-2}
$