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

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

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

We move all terms to the left:

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

We multiply parentheses

-4x^2-12x-(2x-17)+1=0

We get rid of parentheses

-4x^2-12x-2x+17+1=0

We add all the numbers together, and all the variables

-4x^2-14x+18=0

a = -4; b = -14; c = +18;
Δ = b2-4ac
Δ = -142-4·(-4)·18
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{-(-14)-22}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+22}{2*-4}=\frac{36}{-8}
=-4+1/2
$