X^2+x-2=2.25

Solution for X^2+x-2=2.25 equation:

X^2+X-2=2.25

We move all terms to the left:

X^2+X-2-(2.25)=0

We add all the numbers together, and all the variables

X^2+X-4.25=0

a = 1; b = 1; c = -4.25;
Δ = b2-4ac
Δ = 12-4·1·(-4.25)
Δ = 18
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18}=\sqrt{9*2}=\sqrt{9}*\sqrt{2}=3\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{2}}{2*1}=\frac{-1-3\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{2}}{2*1}=\frac{-1+3\sqrt{2}}{2}
$