c(c+8)=9

Solution for c(c+8)=9 equation:

c(c+8)=9

We move all terms to the left:

c(c+8)-(9)=0

We multiply parentheses

c^2+8c-9=0

a = 1; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·1·(-9)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*1}=\frac{-18}{2}
=-9
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*1}=\frac{2}{2}
=1
$