3(x+1)-5x=x^2-12-(6x+7)

Solution for 3(x+1)-5x=x^2-12-(6x+7) equation:

3(x+1)-5x=x^2-12-(6x+7)

We move all terms to the left:

3(x+1)-5x-(x^2-12-(6x+7))=0

We add all the numbers together, and all the variables

-5x+3(x+1)-(x^2-12-(6x+7))=0

We multiply parentheses

-5x+3x-(x^2-12-(6x+7))+3=0


We calculate terms in parentheses: -(x^2-12-(6x+7)), so:

x^2-12-(6x+7)

determiningTheFunctionDomain
x^2-(6x+7)-12

We get rid of parentheses

x^2-6x-7-12

We add all the numbers together, and all the variables

x^2-6x-19

Back to the equation:

-(x^2-6x-19)


We add all the numbers together, and all the variables

-2x-(x^2-6x-19)+3=0

We get rid of parentheses

-x^2-2x+6x+19+3=0

We add all the numbers together, and all the variables

-1x^2+4x+22=0

a = -1; b = 4; c = +22;
Δ = b2-4ac
Δ = 42-4·(-1)·22
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{26}}{2*-1}=\frac{-4-2\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{26}}{2*-1}=\frac{-4+2\sqrt{26}}{-2}
$