x-17=2/3(x)

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

x-17=2/3(x)

We move all terms to the left:

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

We get rid of parentheses

x-2/3x-17=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-51x-2=0

a = 3; b = -51; c = -2;
Δ = b2-4ac
Δ = -512-4·3·(-2)
Δ = 2625
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:

$\sqrt{\Delta}=\sqrt{2625}=\sqrt{25*105}=\sqrt{25}*\sqrt{105}=5\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-5\sqrt{105}}{2*3}=\frac{51-5\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+5\sqrt{105}}{2*3}=\frac{51+5\sqrt{105}}{6}
$