3/4x+2x-3=-1/4x=21

Solution for 3/4x+2x-3=-1/4x=21 equation:

3/4x+2x-3=-1/4x=21

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x*4x-3*4x+4=0

Wy multiply elements

8x^2-12x+4=0

a = 8; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·8·4
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{-(-12)-4}{2*8}=\frac{8}{16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*8}=\frac{16}{16}
=1
$