3/2x-6=1/4x+4

Solution for 3/2x-6=1/4x+4 equation:

3/2x-6=1/4x+4

We move all terms to the left:

3/2x-6-(1/4x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/2x-1/4x-4-6=0

We calculate fractions


12x/8x^2+(-2x)/8x^2-4-6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-80x^2+12x+(-2x)=0

We get rid of parentheses

-80x^2+12x-2x=0

We add all the numbers together, and all the variables

-80x^2+10x=0

a = -80; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-80)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-80}=\frac{-20}{-160}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-80}=\frac{0}{-160}
=0
$