2/3x=x-17

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

2/3x=x-17

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-x+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}
$