10/9+6/5x=2/3x+2

Solution for 10/9+6/5x=2/3x+2 equation:

10/9+6/5x=2/3x+2

We move all terms to the left:

10/9+6/5x-(2/3x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

6/5x-2/3x-2+10/9=0

We calculate fractions


450x^2/1215x^2+1458x/1215x^2+(-810x)/1215x^2-2=0

We multiply all the terms by the denominator


450x^2+1458x+(-810x)-2*1215x^2=0

Wy multiply elements

450x^2-2430x^2+1458x+(-810x)=0

We get rid of parentheses

450x^2-2430x^2+1458x-810x=0

We add all the numbers together, and all the variables

-1980x^2+648x=0

a = -1980; b = 648; c = 0;
Δ = b2-4ac
Δ = 6482-4·(-1980)·0
Δ = 419904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{419904}=648$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(648)-648}{2*-1980}=\frac{-1296}{-3960}
=18/55
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(648)+648}{2*-1980}=\frac{0}{-3960}
=0
$