-x^2+5,x=3

Solution for -x^2+5,x=3 equation:

-x^2+5.x=3

We move all terms to the left:

-x^2+5.x-(3)=0

We add all the numbers together, and all the variables

-1x^2+5.x-3=0

a = -1; b = 5.; c = -3;
Δ = b2-4ac
Δ = 5.2-4·(-1)·(-3)
Δ = 13
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{-(5.)-\sqrt{13}}{2*-1}=\frac{-5-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.)+\sqrt{13}}{2*-1}=\frac{-5+\sqrt{13}}{-2}
$