-x^2+21x-107=0

Solution for -x^2+21x-107=0 equation:

-x^2+21x-107=0

We add all the numbers together, and all the variables

-1x^2+21x-107=0

a = -1; b = 21; c = -107;
Δ = b2-4ac
Δ = 212-4·(-1)·(-107)
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{-(21)-\sqrt{13}}{2*-1}=\frac{-21-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{13}}{2*-1}=\frac{-21+\sqrt{13}}{-2}
$