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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2+3x-(4x+17)=0

We get rid of parentheses

6x^2+3x-4x-17=0

We add all the numbers together, and all the variables

6x^2-1x-17=0

a = 6; b = -1; c = -17;
Δ = b2-4ac
Δ = -12-4·6·(-17)
Δ = 409
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{-(-1)-\sqrt{409}}{2*6}=\frac{1-\sqrt{409}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{409}}{2*6}=\frac{1+\sqrt{409}}{12}
$