5/4x+6=4/3x

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

5/4x+6=4/3x

We move all terms to the left:

5/4x+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

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

We get rid of parentheses

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

We calculate fractions


15x/12x^2+(-16x)/12x^2+6=0

We multiply all the terms by the denominator


15x+(-16x)+6*12x^2=0

Wy multiply elements

72x^2+15x+(-16x)=0

We get rid of parentheses

72x^2+15x-16x=0

We add all the numbers together, and all the variables

72x^2-1x=0

a = 72; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·72·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*72}=\frac{2}{144}
=1/72
$