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: 36x!=0

x!=0/36

x!=0

x∈R


We get rid of parentheses

2/36x-2x-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}
$