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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-8x-18x-(-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 add all the numbers together, and all the variables

3x^2-26x-(10x+3)=0

We get rid of parentheses

3x^2-26x-10x-3=0

We add all the numbers together, and all the variables

3x^2-36x-3=0

a = 3; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·3·(-3)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{37}}{2*3}=\frac{36-6\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{37}}{2*3}=\frac{36+6\sqrt{37}}{6}
$