x=3x-4/4x+3

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

x=3x-4/4x+3

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -8; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·(-8)·4
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{17}}{2*-8}=\frac{12-4\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{17}}{2*-8}=\frac{12+4\sqrt{17}}{-16}
$