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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3/5x-6/7x+3-5/9=0

We calculate fractions


(-1225x^2)/2835x^2+(-1701x)/2835x^2+(-2430x)/2835x^2+3=0

We multiply all the terms by the denominator


(-1225x^2)+(-1701x)+(-2430x)+3*2835x^2=0

Wy multiply elements

(-1225x^2)+8505x^2+(-1701x)+(-2430x)=0

We get rid of parentheses

-1225x^2+8505x^2-1701x-2430x=0

We add all the numbers together, and all the variables

7280x^2-4131x=0

a = 7280; b = -4131; c = 0;
Δ = b2-4ac
Δ = -41312-4·7280·0
Δ = 17065161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17065161}=4131$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4131)-4131}{2*7280}=\frac{0}{14560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4131)+4131}{2*7280}=\frac{8262}{14560}
=4131/7280
$