3-x=3/4x

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

3-x=3/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+12x-3=0

a = -4; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·(-4)·(-3)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{6}}{2*-4}=\frac{-12-4\sqrt{6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{6}}{2*-4}=\frac{-12+4\sqrt{6}}{-8}
$