3k(1-k)+5(k+1)=0

Solution for 3k(1-k)+5(k+1)=0 equation:

3k(1-k)+5(k+1)=0

We add all the numbers together, and all the variables

3k(-1k+1)+5(k+1)=0

We multiply parentheses

-3k^2+3k+5k+5=0

We add all the numbers together, and all the variables

-3k^2+8k+5=0

a = -3; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-3)·5
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{31}}{2*-3}=\frac{-8-2\sqrt{31}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{31}}{2*-3}=\frac{-8+2\sqrt{31}}{-6}
$