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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2+12x-(3x+17)=0

We get rid of parentheses

4x^2+12x-3x-17=0

We add all the numbers together, and all the variables

4x^2+9x-17=0

a = 4; b = 9; c = -17;
Δ = b2-4ac
Δ = 92-4·4·(-17)
Δ = 353
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{-(9)-\sqrt{353}}{2*4}=\frac{-9-\sqrt{353}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{353}}{2*4}=\frac{-9+\sqrt{353}}{8}
$