2/3x=x-30

Solution for 2/3x=x-30 equation:

2/3x=x-30

We move all terms to the left:

2/3x-(x-30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-x+30=0

We multiply all the terms by the denominator


-x*3x+30*3x+2=0

Wy multiply elements

-3x^2+90x+2=0

a = -3; b = 90; c = +2;
Δ = b2-4ac
Δ = 902-4·(-3)·2
Δ = 8124
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:

$\sqrt{\Delta}=\sqrt{8124}=\sqrt{4*2031}=\sqrt{4}*\sqrt{2031}=2\sqrt{2031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2031}}{2*-3}=\frac{-90-2\sqrt{2031}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2031}}{2*-3}=\frac{-90+2\sqrt{2031}}{-6}
$