-x^2+9x+5=-3

Solution for -x^2+9x+5=-3 equation:

-x^2+9x+5=-3

We move all terms to the left:

-x^2+9x+5-(-3)=0

We add all the numbers together, and all the variables

-1x^2+9x+8=0

a = -1; b = 9; c = +8;
Δ = b2-4ac
Δ = 92-4·(-1)·8
Δ = 113
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{-(9)-\sqrt{113}}{2*-1}=\frac{-9-\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{113}}{2*-1}=\frac{-9+\sqrt{113}}{-2}
$