-3x(x+4)+x+1=-23

Solution for -3x(x+4)+x+1=-23 equation:

-3x(x+4)+x+1=-23

We move all terms to the left:

-3x(x+4)+x+1-(-23)=0

We add all the numbers together, and all the variables

x-3x(x+4)+24=0

We multiply parentheses

-3x^2+x-12x+24=0

We add all the numbers together, and all the variables

-3x^2-11x+24=0

a = -3; b = -11; c = +24;
Δ = b2-4ac
Δ = -112-4·(-3)·24
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{-(-11)-\sqrt{409}}{2*-3}=\frac{11-\sqrt{409}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{409}}{2*-3}=\frac{11+\sqrt{409}}{-6}
$