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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/8x^2+(-8x)/8x^2+7+5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

96x^2+12x+(-8x)=0

We get rid of parentheses

96x^2+12x-8x=0

We add all the numbers together, and all the variables

96x^2+4x=0

a = 96; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·96·0
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*96}=\frac{-8}{192}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*96}=\frac{0}{192}
=0
$