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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-162x^2)/72x^2+60x/72x^2+168x/72x^2=0

We multiply all the terms by the denominator


(-162x^2)+60x+168x=0

We add all the numbers together, and all the variables

(-162x^2)+228x=0

We get rid of parentheses

-162x^2+228x=0

a = -162; b = 228; c = 0;
Δ = b2-4ac
Δ = 2282-4·(-162)·0
Δ = 51984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51984}=228$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(228)-228}{2*-162}=\frac{-456}{-324}
=1+11/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(228)+228}{2*-162}=\frac{0}{-324}
=0
$