2/3x=x-15

Solution for 2/3x=x-15 equation:

2/3x=x-15

We move all terms to the left:

2/3x-(x-15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-x+15=0

We multiply all the terms by the denominator


-x*3x+15*3x+2=0

Wy multiply elements

-3x^2+45x+2=0

a = -3; b = 45; c = +2;
Δ = b2-4ac
Δ = 452-4·(-3)·2
Δ = 2049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2049}}{2*-3}=\frac{-45-\sqrt{2049}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2049}}{2*-3}=\frac{-45+\sqrt{2049}}{-6}
$