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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

12-(6x-7)

determiningTheFunctionDomain
-(6x-7)+12

We get rid of parentheses

-6x+7+12

We add all the numbers together, and all the variables

-6x+19

Back to the equation:

-(-6x+19)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+4x-19=0

a = 3; b = 4; c = -19;
Δ = b2-4ac
Δ = 42-4·3·(-19)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{61}}{2*3}=\frac{-4-2\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{61}}{2*3}=\frac{-4+2\sqrt{61}}{6}
$