x^2+21x=11-x^2

Solution for x^2+21x=11-x^2 equation:

x^2+21x=11-x^2

We move all terms to the left:

x^2+21x-(11-x^2)=0

We get rid of parentheses

x^2+x^2+21x-11=0

We add all the numbers together, and all the variables

2x^2+21x-11=0

a = 2; b = 21; c = -11;
Δ = b2-4ac
Δ = 212-4·2·(-11)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-23}{2*2}=\frac{-44}{4}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+23}{2*2}=\frac{2}{4}
=1/2
$