1/2x-3/5=7/4x+1

Solution for 1/2x-3/5=7/4x+1 equation:

1/2x-3/5=7/4x+1

We move all terms to the left:

1/2x-3/5-(7/4x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

1/2x-7/4x-1-3/5=0

We calculate fractions


(-96x^2)/200x^2+100x/200x^2+(-350x)/200x^2-1=0

We multiply all the terms by the denominator


(-96x^2)+100x+(-350x)-1*200x^2=0

Wy multiply elements

(-96x^2)-200x^2+100x+(-350x)=0

We get rid of parentheses

-96x^2-200x^2+100x-350x=0

We add all the numbers together, and all the variables

-296x^2-250x=0

a = -296; b = -250; c = 0;
Δ = b2-4ac
Δ = -2502-4·(-296)·0
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-250}{2*-296}=\frac{0}{-592}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+250}{2*-296}=\frac{500}{-592}
=-125/148
$