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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2-8x-6x-(-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

x^2-14x-(10x+3)=0

We get rid of parentheses

x^2-14x-10x-3=0

We add all the numbers together, and all the variables

x^2-24x-3=0

a = 1; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·1·(-3)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-14\sqrt{3}}{2*1}=\frac{24-14\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+14\sqrt{3}}{2*1}=\frac{24+14\sqrt{3}}{2}
$