6(5x-3)=(1/3)(24x+12)

Solution for 6(5x-3)=(1/3)(24x+12) equation:

6(5x-3)=(1/3)(24x+12)

We move all terms to the left:

6(5x-3)-((1/3)(24x+12))=0


Domain of the equation: 3)(24x+12))!=0

x∈R


We add all the numbers together, and all the variables

6(5x-3)-((+1/3)(24x+12))=0

We multiply parentheses

30x-((+1/3)(24x+12))-18=0

We multiply parentheses ..

-((+24x^2+1/3*12))+30x-18=0

We multiply all the terms by the denominator


-((+24x^2+1+30x*3*12))-18*3*12))=0


We calculate terms in parentheses: -((+24x^2+1+30x*3*12)), so:

(+24x^2+1+30x*3*12)

We get rid of parentheses

24x^2+30x*3*12+1

Wy multiply elements

24x^2+1080x*1+1

Wy multiply elements

24x^2+1080x+1

Back to the equation:

-(24x^2+1080x+1)


We add all the numbers together, and all the variables

-(24x^2+1080x+1)=0

We get rid of parentheses

-24x^2-1080x-1=0

a = -24; b = -1080; c = -1;
Δ = b2-4ac
Δ = -10802-4·(-24)·(-1)
Δ = 1166304
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:

$\sqrt{\Delta}=\sqrt{1166304}=\sqrt{16*72894}=\sqrt{16}*\sqrt{72894}=4\sqrt{72894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-4\sqrt{72894}}{2*-24}=\frac{1080-4\sqrt{72894}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+4\sqrt{72894}}{2*-24}=\frac{1080+4\sqrt{72894}}{-48}
$