2/3x=x-62

Solution for 2/3x=x-62 equation:

2/3x=x-62

We move all terms to the left:

2/3x-(x-62)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-x+62=0

We multiply all the terms by the denominator


-x*3x+62*3x+2=0

Wy multiply elements

-3x^2+186x+2=0

a = -3; b = 186; c = +2;
Δ = b2-4ac
Δ = 1862-4·(-3)·2
Δ = 34620
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:

$\sqrt{\Delta}=\sqrt{34620}=\sqrt{4*8655}=\sqrt{4}*\sqrt{8655}=2\sqrt{8655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(186)-2\sqrt{8655}}{2*-3}=\frac{-186-2\sqrt{8655}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(186)+2\sqrt{8655}}{2*-3}=\frac{-186+2\sqrt{8655}}{-6}
$