1/2x-5+2/3=7/6x+4

Solution for 1/2x-5+2/3=7/6x+4 equation:

1/2x-5+2/3=7/6x+4

We move all terms to the left:

1/2x-5+2/3-(7/6x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+4)!=0

x∈R


We get rid of parentheses

1/2x-7/6x-4-5+2/3=0

We calculate fractions


144x^2/108x^2+54x/108x^2+(-126x)/108x^2-4-5=0

We add all the numbers together, and all the variables

144x^2/108x^2+54x/108x^2+(-126x)/108x^2-9=0

We multiply all the terms by the denominator


144x^2+54x+(-126x)-9*108x^2=0

Wy multiply elements

144x^2-972x^2+54x+(-126x)=0

We get rid of parentheses

144x^2-972x^2+54x-126x=0

We add all the numbers together, and all the variables

-828x^2-72x=0

a = -828; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·(-828)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*-828}=\frac{0}{-1656}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*-828}=\frac{144}{-1656}
=-2/23
$