3/4x+1/4x=x

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

3/4x+1/4x=x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1x*4x+4=0

Wy multiply elements

-4x^2+4=0

a = -4; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-4)·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-4}=\frac{8}{-8}
=-1
$