-x^2+9x+52=0

Solution for -x^2+9x+52=0 equation:

-x^2+9x+52=0

We add all the numbers together, and all the variables

-1x^2+9x+52=0

a = -1; b = 9; c = +52;
Δ = b2-4ac
Δ = 92-4·(-1)·52
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-17}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*-1}=\frac{8}{-2}
=-4
$