84=x^2+x

Solution for 84=x^2+x equation:

84=x^2+x

We move all terms to the left:

84-(x^2+x)=0

We get rid of parentheses

-x^2-x+84=0

We add all the numbers together, and all the variables

-1x^2-1x+84=0

a = -1; b = -1; c = +84;
Δ = b2-4ac
Δ = -12-4·(-1)·84
Δ = 337
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{337}}{2*-1}=\frac{1-\sqrt{337}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{337}}{2*-1}=\frac{1+\sqrt{337}}{-2}
$