2/3x+30=2x

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

2/3x+30=2x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+90x+2=0

a = -6; b = 90; c = +2;
Δ = b2-4ac
Δ = 902-4·(-6)·2
Δ = 8148
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:

$\sqrt{\Delta}=\sqrt{8148}=\sqrt{4*2037}=\sqrt{4}*\sqrt{2037}=2\sqrt{2037}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2037}}{2*-6}=\frac{-90-2\sqrt{2037}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2037}}{2*-6}=\frac{-90+2\sqrt{2037}}{-12}
$