22x2-9x-31=0

Solution for 22x2-9x-31=0 equation:

22x^2-9x-31=0

a = 22; b = -9; c = -31;
Δ = b2-4ac
Δ = -92-4·22·(-31)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-53}{2*22}=\frac{-44}{44}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+53}{2*22}=\frac{62}{44}
=1+9/22
$