2x^2+1x-22.5=0

Solution for 2x^2+1x-22.5=0 equation:

2x^2+1x-22.5=0

We add all the numbers together, and all the variables

2x^2+x-22.5=0

a = 2; b = 1; c = -22.5;
Δ = b2-4ac
Δ = 12-4·2·(-22.5)
Δ = 181
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{-(1)-\sqrt{181}}{2*2}=\frac{-1-\sqrt{181}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{181}}{2*2}=\frac{-1+\sqrt{181}}{4}
$