31x-x^2-198=0

Solution for 31x-x^2-198=0 equation:

31x-x^2-198=0

We add all the numbers together, and all the variables

-1x^2+31x-198=0

a = -1; b = 31; c = -198;
Δ = b2-4ac
Δ = 312-4·(-1)·(-198)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-13}{2*-1}=\frac{-44}{-2}
=+22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+13}{2*-1}=\frac{-18}{-2}
=+9
$