37.5=x^2+x

Solution for 37.5=x^2+x equation:

37.5=x^2+x

We move all terms to the left:

37.5-(x^2+x)=0

We get rid of parentheses

-x^2-x+37.5=0

We add all the numbers together, and all the variables

-1x^2-1x+37.5=0

a = -1; b = -1; c = +37.5;
Δ = b2-4ac
Δ = -12-4·(-1)·37.5
Δ = 151
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{151}}{2*-1}=\frac{1-\sqrt{151}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{151}}{2*-1}=\frac{1+\sqrt{151}}{-2}
$