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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


54x^2/72x^2+60x/72x^2+(-96x)/72x^2+7=0

We multiply all the terms by the denominator


54x^2+60x+(-96x)+7*72x^2=0

Wy multiply elements

54x^2+504x^2+60x+(-96x)=0

We get rid of parentheses

54x^2+504x^2+60x-96x=0

We add all the numbers together, and all the variables

558x^2-36x=0

a = 558; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·558·0
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*558}=\frac{0}{1116}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*558}=\frac{72}{1116}
=2/31
$