100-3x(8+x)=1

Solution for 100-3x(8+x)=1 equation:

100-3x(8+x)=1

We move all terms to the left:

100-3x(8+x)-(1)=0

We add all the numbers together, and all the variables

-3x(x+8)+100-1=0

We add all the numbers together, and all the variables

-3x(x+8)+99=0

We multiply parentheses

-3x^2-24x+99=0

a = -3; b = -24; c = +99;
Δ = b2-4ac
Δ = -242-4·(-3)·99
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-42}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+42}{2*-3}=\frac{66}{-6}
=-11
$