x+4/4=5-(x+2)/3

Solution for x+4/4=5-(x+2)/3 equation:

x+4/4=5-(x+2)/3

We move all terms to the left:

x+4/4-(5-(x+2)/3)=0

We add all the numbers together, and all the variables

x-(5-(x+2)/3)+1=0

We multiply all the terms by the denominator


x*3)-(5-(x+2)+1*3)=0

We add all the numbers together, and all the variables

x*3)-(5-(x+2)=0

Wy multiply elements

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

We get rid of parentheses

3x^2-x-2=0

We add all the numbers together, and all the variables

3x^2-1x-2=0

a = 3; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·3·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*3}=\frac{-4}{6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*3}=\frac{6}{6}
=1
$