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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-48x^2)/432x^2+288x/432x^2+540x/432x^2-5=0

We multiply all the terms by the denominator


(-48x^2)+288x+540x-5*432x^2=0

We add all the numbers together, and all the variables

(-48x^2)+828x-5*432x^2=0

Wy multiply elements

(-48x^2)-2160x^2+828x=0

We get rid of parentheses

-48x^2-2160x^2+828x=0

We add all the numbers together, and all the variables

-2208x^2+828x=0

a = -2208; b = 828; c = 0;
Δ = b2-4ac
Δ = 8282-4·(-2208)·0
Δ = 685584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{685584}=828$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(828)-828}{2*-2208}=\frac{-1656}{-4416}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(828)+828}{2*-2208}=\frac{0}{-4416}
=0
$