8k2=-2+17k

Solution for 8k2=-2+17k equation:

8k^2=-2+17k

We move all terms to the left:

8k^2-(-2+17k)=0

We add all the numbers together, and all the variables

8k^2-(17k-2)=0

We get rid of parentheses

8k^2-17k+2=0

a = 8; b = -17; c = +2;
Δ = b2-4ac
Δ = -172-4·8·2
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-15}{2*8}=\frac{2}{16}
=1/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+15}{2*8}=\frac{32}{16}
=2
$