X^2+4x+2=22

Solution for X^2+4x+2=22 equation:

X^2+4X+2=22

We move all terms to the left:

X^2+4X+2-(22)=0

We add all the numbers together, and all the variables

X^2+4X-20=0

a = 1; b = 4; c = -20;
Δ = b2-4ac
Δ = 42-4·1·(-20)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*1}=\frac{-4-4\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*1}=\frac{-4+4\sqrt{6}}{2}
$