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

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

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

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

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

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+2=0

Wy multiply elements

8x^2+12x+2=0

a = 8; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·8·2
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{5}}{2*8}=\frac{-12-4\sqrt{5}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{5}}{2*8}=\frac{-12+4\sqrt{5}}{16}
$