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

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

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

We move all terms to the left:

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

We calculate fractions


12x/8x^2+(-6x)/8x^2-7-5=0

We add all the numbers together, and all the variables

12x/8x^2+(-6x)/8x^2-12=0

We multiply all the terms by the denominator


12x+(-6x)-12*8x^2=0

Wy multiply elements

-96x^2+12x+(-6x)=0

We get rid of parentheses

-96x^2+12x-6x=0

We add all the numbers together, and all the variables

-96x^2+6x=0

a = -96; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-96)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-96}=\frac{-12}{-192}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-96}=\frac{0}{-192}
=0
$