X-6=4/3x

Solution for X-6=4/3x equation:

X-6=4/3X

We move all terms to the left:

X-6-(4/3X)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+4/3X)-6=0

We get rid of parentheses

X-4/3X-6=0

We multiply all the terms by the denominator


X*3X-6*3X-4=0

Wy multiply elements

3X^2-18X-4=0

a = 3; b = -18; c = -4;
Δ = b2-4ac
Δ = -182-4·3·(-4)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*3}=\frac{18-2\sqrt{93}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*3}=\frac{18+2\sqrt{93}}{6}
$