5x=(2/3)(6x+12)

Solution for 5x=(2/3)(6x+12) equation:

5x=(2/3)(6x+12)

We move all terms to the left:

5x-((2/3)(6x+12))=0


Domain of the equation: 3)(6x+12))!=0

x∈R


We add all the numbers together, and all the variables

5x-((+2/3)(6x+12))=0

We multiply parentheses ..

-((+12x^2+2/3*12))+5x=0

We multiply all the terms by the denominator


-((+12x^2+2+5x*3*12))=0


We calculate terms in parentheses: -((+12x^2+2+5x*3*12)), so:

(+12x^2+2+5x*3*12)

We get rid of parentheses

12x^2+5x*3*12+2

Wy multiply elements

12x^2+180x*1+2

Wy multiply elements

12x^2+180x+2

Back to the equation:

-(12x^2+180x+2)


We get rid of parentheses

-12x^2-180x-2=0

a = -12; b = -180; c = -2;
Δ = b2-4ac
Δ = -1802-4·(-12)·(-2)
Δ = 32304
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:

$\sqrt{\Delta}=\sqrt{32304}=\sqrt{16*2019}=\sqrt{16}*\sqrt{2019}=4\sqrt{2019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-4\sqrt{2019}}{2*-12}=\frac{180-4\sqrt{2019}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+4\sqrt{2019}}{2*-12}=\frac{180+4\sqrt{2019}}{-24}
$