6x-(5x+5)=-8-2x(x+12)

Solution for 6x-(5x+5)=-8-2x(x+12) equation:

6x-(5x+5)=-8-2x(x+12)

We move all terms to the left:

6x-(5x+5)-(-8-2x(x+12))=0

We get rid of parentheses

6x-5x-(-8-2x(x+12))-5=0


We calculate terms in parentheses: -(-8-2x(x+12)), so:

-8-2x(x+12)

determiningTheFunctionDomain
-2x(x+12)-8

We multiply parentheses

-2x^2-24x-8

Back to the equation:

-(-2x^2-24x-8)


We add all the numbers together, and all the variables

-(-2x^2-24x-8)+x-5=0

We get rid of parentheses

2x^2+24x+x+8-5=0

We add all the numbers together, and all the variables

2x^2+25x+3=0

a = 2; b = 25; c = +3;
Δ = b2-4ac
Δ = 252-4·2·3
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{601}}{2*2}=\frac{-25-\sqrt{601}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{601}}{2*2}=\frac{-25+\sqrt{601}}{4}
$