x+9/5x-1=x+7/2x-3

Solution for x+9/5x-1=x+7/2x-3 equation:

x+9/5x-1=x+7/2x-3

We move all terms to the left:

x+9/5x-1-(x+7/2x-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

x+9/5x-x-7/2x+3-1=0

We calculate fractions


x-x+18x/10x^2+(-35x)/10x^2+3-1=0

We add all the numbers together, and all the variables

18x/10x^2+(-35x)/10x^2+2=0

We multiply all the terms by the denominator


18x+(-35x)+2*10x^2=0

Wy multiply elements

20x^2+18x+(-35x)=0

We get rid of parentheses

20x^2+18x-35x=0

We add all the numbers together, and all the variables

20x^2-17x=0

a = 20; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·20·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*20}=\frac{34}{40}
=17/20
$