(3/5)x-3/7=5/7

Solution for (3/5)x-3/7=5/7 equation:

(3/5)x-3/7=5/7

We move all terms to the left:

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


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

3x^2-3/7-5/7=0

We multiply all the terms by the denominator


3x^2*7-3-5=0

We add all the numbers together, and all the variables

3x^2*7-8=0

Wy multiply elements

21x^2-8=0

a = 21; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·21·(-8)
Δ = 672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*21}=\frac{0-4\sqrt{42}}{42}
=-\frac{4\sqrt{42}}{42}
=-\frac{2\sqrt{42}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*21}=\frac{0+4\sqrt{42}}{42}
=\frac{4\sqrt{42}}{42}
=\frac{2\sqrt{42}}{21}
$