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

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

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

We move all terms to the left:

7x/5-(3x/2x+1)=0


Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


14x^2/10x+(-15x)/10x-1=0

We multiply all the terms by the denominator


14x^2+(-15x)-1*10x=0

Wy multiply elements

14x^2+(-15x)-10x=0

We get rid of parentheses

14x^2-15x-10x=0

We add all the numbers together, and all the variables

14x^2-25x=0

a = 14; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·14·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*14}=\frac{50}{28}
=1+11/14
$