2x+30=2/3(6x)

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

2x+30=2/3(6x)

We move all terms to the left:

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


Domain of the equation: 36x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+2/36x)+30=0

We get rid of parentheses

2x-2/36x+30=0

We multiply all the terms by the denominator


2x*36x+30*36x-2=0

Wy multiply elements

72x^2+1080x-2=0

a = 72; b = 1080; c = -2;
Δ = b2-4ac
Δ = 10802-4·72·(-2)
Δ = 1166976
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:

$\sqrt{\Delta}=\sqrt{1166976}=\sqrt{576*2026}=\sqrt{576}*\sqrt{2026}=24\sqrt{2026}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1080)-24\sqrt{2026}}{2*72}=\frac{-1080-24\sqrt{2026}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1080)+24\sqrt{2026}}{2*72}=\frac{-1080+24\sqrt{2026}}{144}
$