4/5x-22/3=3/4x

Solution for 4/5x-22/3=3/4x equation:

4/5x-22/3=3/4x

We move all terms to the left:

4/5x-22/3-(3/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(+3/4x)-22/3=0

We get rid of parentheses

4/5x-3/4x-22/3=0

We calculate fractions


(-1760x^2)/180x^2+144x/180x^2+(-135x)/180x^2=0

We multiply all the terms by the denominator


(-1760x^2)+144x+(-135x)=0

We get rid of parentheses

-1760x^2+144x-135x=0

We add all the numbers together, and all the variables

-1760x^2+9x=0

a = -1760; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-1760)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-1760}=\frac{-18}{-3520}
=9/1760
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-1760}=\frac{0}{-3520}
=0
$