5-x(x+8)2=x-4

Solution for 5-x(x+8)2=x-4 equation:

5-x(x+8)2=x-4

We move all terms to the left:

5-x(x+8)2-(x-4)=0

We multiply parentheses

-2x^2-16x-(x-4)+5=0

We get rid of parentheses

-2x^2-16x-x+4+5=0

We add all the numbers together, and all the variables

-2x^2-17x+9=0

a = -2; b = -17; c = +9;
Δ = b2-4ac
Δ = -172-4·(-2)·9
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-19}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+19}{2*-2}=\frac{36}{-4}
=-9
$