3(x-6)8x=-2+5(2x+1)

Solution for 3(x-6)8x=-2+5(2x+1) equation:

3(x-6)8x=-2+5(2x+1)

We move all terms to the left:

3(x-6)8x-(-2+5(2x+1))=0

We multiply parentheses

24x^2-144x-(-2+5(2x+1))=0


We calculate terms in parentheses: -(-2+5(2x+1)), so:

-2+5(2x+1)

determiningTheFunctionDomain
5(2x+1)-2

We multiply parentheses

10x+5-2

We add all the numbers together, and all the variables

10x+3

Back to the equation:

-(10x+3)


We get rid of parentheses

24x^2-144x-10x-3=0

We add all the numbers together, and all the variables

24x^2-154x-3=0

a = 24; b = -154; c = -3;
Δ = b2-4ac
Δ = -1542-4·24·(-3)
Δ = 24004
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:

$\sqrt{\Delta}=\sqrt{24004}=\sqrt{4*6001}=\sqrt{4}*\sqrt{6001}=2\sqrt{6001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{6001}}{2*24}=\frac{154-2\sqrt{6001}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{6001}}{2*24}=\frac{154+2\sqrt{6001}}{48}
$