X2+2x+6=-3x+2

Solution for X2+2x+6=-3x+2 equation:

X2+2X+6=-3X+2

We move all terms to the left:

X2+2X+6-(-3X+2)=0

We add all the numbers together, and all the variables

X^2+2X-(-3X+2)+6=0

We get rid of parentheses

X^2+2X+3X-2+6=0

We add all the numbers together, and all the variables

X^2+5X+4=0

a = 1; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*1}=\frac{-2}{2}
=-1
$