3(x+2)=x2

Solution for 3(x+2)=x2 equation:

3(x+2)=x2

We move all terms to the left:

3(x+2)-(x2)=0

We add all the numbers together, and all the variables

-1x^2+3(x+2)=0

We multiply parentheses

-1x^2+3x+6=0

a = -1; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-1)·6
Δ = 33
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{-(3)-\sqrt{33}}{2*-1}=\frac{-3-\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*-1}=\frac{-3+\sqrt{33}}{-2}
$