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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/8x^2+(-10x)/8x^2-3+1=0

We add all the numbers together, and all the variables

12x/8x^2+(-10x)/8x^2-2=0

We multiply all the terms by the denominator


12x+(-10x)-2*8x^2=0

Wy multiply elements

-16x^2+12x+(-10x)=0

We get rid of parentheses

-16x^2+12x-10x=0

We add all the numbers together, and all the variables

-16x^2+2x=0

a = -16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-16)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-16}=\frac{-4}{-32}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-16}=\frac{0}{-32}
=0
$