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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-4x^2-12x+8x+2=0

We add all the numbers together, and all the variables

-4x^2-4x+2=0

a = -4; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-4)·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*-4}=\frac{4-4\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*-4}=\frac{4+4\sqrt{3}}{-8}
$