6(x)=17-2/3x

Solution for 6(x)=17-2/3x equation:

6(x)=17-2/3x

We move all terms to the left:

6(x)-(17-2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(-2/3x+17)=0

We get rid of parentheses

6x+2/3x-17=0

We multiply all the terms by the denominator


6x*3x-17*3x+2=0

Wy multiply elements

18x^2-51x+2=0

a = 18; b = -51; c = +2;
Δ = b2-4ac
Δ = -512-4·18·2
Δ = 2457
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:

$\sqrt{\Delta}=\sqrt{2457}=\sqrt{9*273}=\sqrt{9}*\sqrt{273}=3\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{273}}{2*18}=\frac{51-3\sqrt{273}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{273}}{2*18}=\frac{51+3\sqrt{273}}{36}
$