-x^2+31x-150=0

Solution for -x^2+31x-150=0 equation:

-x^2+31x-150=0

We add all the numbers together, and all the variables

-1x^2+31x-150=0

a = -1; b = 31; c = -150;
Δ = b2-4ac
Δ = 312-4·(-1)·(-150)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-19}{2*-1}=\frac{-50}{-2}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+19}{2*-1}=\frac{-12}{-2}
=+6
$