X^2+x=36.75

Solution for X^2+x=36.75 equation:

X^2+X=36.75

We move all terms to the left:

X^2+X-(36.75)=0

We add all the numbers together, and all the variables

X^2+X-36.75=0

a = 1; b = 1; c = -36.75;
Δ = b2-4ac
Δ = 12-4·1·(-36.75)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-2\sqrt{37}}{2*1}=\frac{-1-2\sqrt{37}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+2\sqrt{37}}{2*1}=\frac{-1+2\sqrt{37}}{2}
$