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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-8x-18x-(-3-5(2x+1))=0


We calculate terms in parentheses: -(-3-5(2x+1)), so:

-3-5(2x+1)

determiningTheFunctionDomain
-5(2x+1)-3

We multiply parentheses

-10x-5-3

We add all the numbers together, and all the variables

-10x-8

Back to the equation:

-(-10x-8)


We add all the numbers together, and all the variables

3x^2-26x-(-10x-8)=0

We get rid of parentheses

3x^2-26x+10x+8=0

We add all the numbers together, and all the variables

3x^2-16x+8=0

a = 3; b = -16; c = +8;
Δ = b2-4ac
Δ = -162-4·3·8
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{10}}{2*3}=\frac{16-4\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{10}}{2*3}=\frac{16+4\sqrt{10}}{6}
$