2c^2+17c-9=c^2-1c

Solution for 2c^2+17c-9=c^2-1c equation:

2c^2+17c-9=c^2-1c

We move all terms to the left:

2c^2+17c-9-(c^2-1c)=0

We get rid of parentheses

2c^2-c^2+17c+1c-9=0

We add all the numbers together, and all the variables

c^2+18c-9=0

a = 1; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·1·(-9)
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{10}}{2*1}=\frac{-18-6\sqrt{10}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{10}}{2*1}=\frac{-18+6\sqrt{10}}{2}
$