3x(2x+4)-2x+1=17

Solution for 3x(2x+4)-2x+1=17 equation:

3x(2x+4)-2x+1=17

We move all terms to the left:

3x(2x+4)-2x+1-(17)=0

We add all the numbers together, and all the variables

-2x+3x(2x+4)-16=0

We multiply parentheses

6x^2-2x+12x-16=0

We add all the numbers together, and all the variables

6x^2+10x-16=0

a = 6; b = 10; c = -16;
Δ = b2-4ac
Δ = 102-4·6·(-16)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-22}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+22}{2*6}=\frac{12}{12}
=1
$