5k(k+2)=15

Solution for 5k(k+2)=15 equation:

5k(k+2)=15

We move all terms to the left:

5k(k+2)-(15)=0

We multiply parentheses

5k^2+10k-15=0

a = 5; b = 10; c = -15;
Δ = b2-4ac
Δ = 102-4·5·(-15)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-20}{2*5}=\frac{-30}{10}
=-3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+20}{2*5}=\frac{10}{10}
=1
$