c+8=17-c2

Solution for c+8=17-c2 equation:

c+8=17-c2

We move all terms to the left:

c+8-(17-c2)=0

We add all the numbers together, and all the variables

-(-1c^2+17)+c+8=0

We get rid of parentheses

1c^2+c-17+8=0

We add all the numbers together, and all the variables

c^2+c-9=0

a = 1; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·1·(-9)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{37}}{2*1}=\frac{-1-\sqrt{37}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*1}=\frac{-1+\sqrt{37}}{2}
$