x2+21x+32=12

Solution for x2+21x+32=12 equation:

x2+21x+32=12

We move all terms to the left:

x2+21x+32-(12)=0

We add all the numbers together, and all the variables

x^2+21x+20=0

a = 1; b = 21; c = +20;
Δ = b2-4ac
Δ = 212-4·1·20
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-19}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+19}{2*1}=\frac{-2}{2}
=-1
$