X^2+x=40.5

Solution for X^2+x=40.5 equation:

X^2+X=40.5

We move all terms to the left:

X^2+X-(40.5)=0

We add all the numbers together, and all the variables

X^2+X-40.5=0

a = 1; b = 1; c = -40.5;
Δ = b2-4ac
Δ = 12-4·1·(-40.5)
Δ = 163
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{163}}{2*1}=\frac{-1-\sqrt{163}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{163}}{2*1}=\frac{-1+\sqrt{163}}{2}
$