8k(k+2)=2k-3

Solution for 8k(k+2)=2k-3 equation:

8k(k+2)=2k-3

We move all terms to the left:

8k(k+2)-(2k-3)=0

We multiply parentheses

8k^2+16k-(2k-3)=0

We get rid of parentheses

8k^2+16k-2k+3=0

We add all the numbers together, and all the variables

8k^2+14k+3=0

a = 8; b = 14; c = +3;
Δ = b2-4ac
Δ = 142-4·8·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*8}=\frac{-24}{16}
=-1+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*8}=\frac{-4}{16}
=-1/4
$