1/4x+7/6=4/3x

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

1/4x+7/6=4/3x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


252x^2/432x^2+108x/432x^2+(-576x)/432x^2=0

We multiply all the terms by the denominator


252x^2+108x+(-576x)=0

We get rid of parentheses

252x^2+108x-576x=0

We add all the numbers together, and all the variables

252x^2-468x=0

a = 252; b = -468; c = 0;
Δ = b2-4ac
Δ = -4682-4·252·0
Δ = 219024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{219024}=468$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-468}{2*252}=\frac{0}{504}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+468}{2*252}=\frac{936}{504}
=1+6/7
$