-4(2b-9)=(1/3)(-24b+108)

Solution for -4(2b-9)=(1/3)(-24b+108) equation:

-4(2b-9)=(1/3)(-24b+108)

We move all terms to the left:

-4(2b-9)-((1/3)(-24b+108))=0


Domain of the equation: 3)(-24b+108))!=0

b∈R


We add all the numbers together, and all the variables

-4(2b-9)-((+1/3)(-24b+108))=0

We multiply parentheses

-8b-((+1/3)(-24b+108))+36=0

We multiply parentheses ..

-((-24b^2+1/3*108))-8b+36=0

We multiply all the terms by the denominator


-((-24b^2+1-8b*3*108))+36*3*108))=0


We calculate terms in parentheses: -((-24b^2+1-8b*3*108)), so:

(-24b^2+1-8b*3*108)

We get rid of parentheses

-24b^2-8b*3*108+1

Wy multiply elements

-24b^2-2592b*1+1

Wy multiply elements

-24b^2-2592b+1

Back to the equation:

-(-24b^2-2592b+1)


We add all the numbers together, and all the variables

-(-24b^2-2592b+1)=0

We get rid of parentheses

24b^2+2592b-1=0

a = 24; b = 2592; c = -1;
Δ = b2-4ac
Δ = 25922-4·24·(-1)
Δ = 6718560
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6718560}=\sqrt{16*419910}=\sqrt{16}*\sqrt{419910}=4\sqrt{419910}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2592)-4\sqrt{419910}}{2*24}=\frac{-2592-4\sqrt{419910}}{48}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2592)+4\sqrt{419910}}{2*24}=\frac{-2592+4\sqrt{419910}}{48}
$