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

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

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

We move all terms to the left:

1/4x+x-(-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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x*4x+3*4x=0

Wy multiply elements

4x^2+12x=0

a = 4; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·4·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*4}=\frac{0}{8}
=0
$