x2+x=21

Solution for x2+x=21 equation:

x2+x=21

We move all terms to the left:

x2+x-(21)=0

We add all the numbers together, and all the variables

x^2+x-21=0

a = 1; b = 1; c = -21;
Δ = b2-4ac
Δ = 12-4·1·(-21)
Δ = 85
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{85}}{2*1}=\frac{-1-\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{85}}{2*1}=\frac{-1+\sqrt{85}}{2}
$