7/5x-9=2/2x-3

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

7/5x-9=2/2x-3

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


14x/10x^2+(-10x)/10x^2+3-9=0

We add all the numbers together, and all the variables

14x/10x^2+(-10x)/10x^2-6=0

We multiply all the terms by the denominator


14x+(-10x)-6*10x^2=0

Wy multiply elements

-60x^2+14x+(-10x)=0

We get rid of parentheses

-60x^2+14x-10x=0

We add all the numbers together, and all the variables

-60x^2+4x=0

a = -60; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-60)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-60}=\frac{-8}{-120}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-60}=\frac{0}{-120}
=0
$