7/8x-2/3=1/6x+3

Solution for 7/8x-2/3=1/6x+3 equation:

7/8x-2/3=1/6x+3

We move all terms to the left:

7/8x-2/3-(1/6x+3)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 6x+3)!=0

x∈R


We get rid of parentheses

7/8x-1/6x-3-2/3=0

We calculate fractions


(-576x^2)/432x^2+378x/432x^2+(-72x)/432x^2-3=0

We multiply all the terms by the denominator


(-576x^2)+378x+(-72x)-3*432x^2=0

Wy multiply elements

(-576x^2)-1296x^2+378x+(-72x)=0

We get rid of parentheses

-576x^2-1296x^2+378x-72x=0

We add all the numbers together, and all the variables

-1872x^2+306x=0

a = -1872; b = 306; c = 0;
Δ = b2-4ac
Δ = 3062-4·(-1872)·0
Δ = 93636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{93636}=306$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(306)-306}{2*-1872}=\frac{-612}{-3744}
=17/104
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(306)+306}{2*-1872}=\frac{0}{-3744}
=0
$