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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

14-2(3x-4)

determiningTheFunctionDomain
-2(3x-4)+14

We multiply parentheses

-6x+8+14

We add all the numbers together, and all the variables

-6x+22

Back to the equation:

-(-6x+22)


We get rid of parentheses

3x^2+3x+6x-22-8=0

We add all the numbers together, and all the variables

3x^2+9x-30=0

a = 3; b = 9; c = -30;
Δ = b2-4ac
Δ = 92-4·3·(-30)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*3}=\frac{12}{6}
=2
$