x=4/3x-4

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

x=4/3x-4

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

x-4/3x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+12x-4=0

a = 3; b = 12; c = -4;
Δ = b2-4ac
Δ = 122-4·3·(-4)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*3}=\frac{-12-8\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*3}=\frac{-12+8\sqrt{3}}{6}
$