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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2x/8x^2+12x/8x^2-3+2=0

We add all the numbers together, and all the variables

2x/8x^2+12x/8x^2-1=0

We multiply all the terms by the denominator


2x+12x-1*8x^2=0

We add all the numbers together, and all the variables

14x-1*8x^2=0

Wy multiply elements

-8x^2+14x=0

a = -8; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-8)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-8}=\frac{-28}{-16}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-8}=\frac{0}{-16}
=0
$