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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-54x^2)/72x^2+84x/72x^2+(-48x)/72x^2-5=0

We multiply all the terms by the denominator


(-54x^2)+84x+(-48x)-5*72x^2=0

Wy multiply elements

(-54x^2)-360x^2+84x+(-48x)=0

We get rid of parentheses

-54x^2-360x^2+84x-48x=0

We add all the numbers together, and all the variables

-414x^2+36x=0

a = -414; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-414)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-414}=\frac{-72}{-828}
=2/23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-414}=\frac{0}{-828}
=0
$