3(x+1)-8=14-2x(3x-4)

Solution for 3(x+1)-8=14-2x(3x-4) equation:

3(x+1)-8=14-2x(3x-4)

We move all terms to the left:

3(x+1)-8-(14-2x(3x-4))=0

We multiply parentheses

3x-(14-2x(3x-4))+3-8=0


We calculate terms in parentheses: -(14-2x(3x-4)), so:

14-2x(3x-4)

determiningTheFunctionDomain
-2x(3x-4)+14

We multiply parentheses

-6x^2+8x+14

Back to the equation:

-(-6x^2+8x+14)


We add all the numbers together, and all the variables

-(-6x^2+8x+14)+3x-5=0

We get rid of parentheses

6x^2-8x+3x-14-5=0

We add all the numbers together, and all the variables

6x^2-5x-19=0

a = 6; b = -5; c = -19;
Δ = b2-4ac
Δ = -52-4·6·(-19)
Δ = 481
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{-(-5)-\sqrt{481}}{2*6}=\frac{5-\sqrt{481}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{481}}{2*6}=\frac{5+\sqrt{481}}{12}
$