X(x+3)-1/2=-2

Solution for X(x+3)-1/2=-2 equation:

X(X+3)-1/2=-2

We move all terms to the left:

X(X+3)-1/2-(-2)=0

We add all the numbers together, and all the variables

X(X+3)+2-1/2=0

We multiply parentheses

X^2+3X+2-1/2=0

We multiply all the terms by the denominator


X^2*2+3X*2-1+2*2=0

We add all the numbers together, and all the variables

X^2*2+3X*2+3=0

Wy multiply elements

2X^2+6X+3=0

a = 2; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·2·3
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*2}=\frac{-6-2\sqrt{3}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*2}=\frac{-6+2\sqrt{3}}{4}
$