9/2x+6-7/5x+15=2/3

Solution for 9/2x+6-7/5x+15=2/3 equation:

9/2x+6-7/5x+15=2/3

We move all terms to the left:

9/2x+6-7/5x+15-(2/3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

9/2x-7/5x+6+15-(+2/3)=0

We add all the numbers together, and all the variables

9/2x-7/5x+21-(+2/3)=0

We get rid of parentheses

9/2x-7/5x+21-2/3=0

We calculate fractions


(-100x^2)/90x^2+405x/90x^2+(-126x)/90x^2+21=0

We multiply all the terms by the denominator


(-100x^2)+405x+(-126x)+21*90x^2=0

Wy multiply elements

(-100x^2)+1890x^2+405x+(-126x)=0

We get rid of parentheses

-100x^2+1890x^2+405x-126x=0

We add all the numbers together, and all the variables

1790x^2+279x=0

a = 1790; b = 279; c = 0;
Δ = b2-4ac
Δ = 2792-4·1790·0
Δ = 77841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{77841}=279$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(279)-279}{2*1790}=\frac{-558}{3580}
=-279/1790
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(279)+279}{2*1790}=\frac{0}{3580}
=0
$