2/3*6x=2x+30

Solution for 2/3*6x=2x+30 equation:

2/3*6x=2x+30

We move all terms to the left:

2/3*6x-(2x+30)=0


Domain of the equation: 3*6x!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

2/3*6x-2x-30=0

We multiply all the terms by the denominator


-2x*3*6x-30*3*6x+2=0

Wy multiply elements

-36x^2*6-540x*6+2=0

Wy multiply elements

-216x^2-3240x+2=0

a = -216; b = -3240; c = +2;
Δ = b2-4ac
Δ = -32402-4·(-216)·2
Δ = 10499328
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:

$\sqrt{\Delta}=\sqrt{10499328}=\sqrt{112896*93}=\sqrt{112896}*\sqrt{93}=336\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3240)-336\sqrt{93}}{2*-216}=\frac{3240-336\sqrt{93}}{-432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3240)+336\sqrt{93}}{2*-216}=\frac{3240+336\sqrt{93}}{-432}
$