3/2x+4-3/4x=12

Solution for 3/2x+4-3/4x=12 equation:

3/2x+4-3/4x=12

We move all terms to the left:

3/2x+4-3/4x-(12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-3/4x-8=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-64x^2+12x+(-6x)=0

We get rid of parentheses

-64x^2+12x-6x=0

We add all the numbers together, and all the variables

-64x^2+6x=0

a = -64; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-64)·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*-64}=\frac{-12}{-128}
=3/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-64}=\frac{0}{-128}
=0
$