2x+21/3=-(x+2)/2

Solution for 2x+21/3=-(x+2)/2 equation:

2x+21/3=-(x+2)/2

We move all terms to the left:

2x+21/3-(-(x+2)/2)=0

We add all the numbers together, and all the variables

2x-(-(x+2)/2)+7=0

We multiply all the terms by the denominator


2x*2)-(-(x+2)+7*2)=0

We add all the numbers together, and all the variables

2x*2)-(-(x+2)=0

Wy multiply elements

4x^2-(x+2)=0

We get rid of parentheses

4x^2-x-2=0

We add all the numbers together, and all the variables

4x^2-1x-2=0

a = 4; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·4·(-2)
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{-(-1)-\sqrt{33}}{2*4}=\frac{1-\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*4}=\frac{1+\sqrt{33}}{8}
$