15k(k+3)=11k-15

Solution for 15k(k+3)=11k-15 equation:

15k(k+3)=11k-15

We move all terms to the left:

15k(k+3)-(11k-15)=0

We multiply parentheses

15k^2+45k-(11k-15)=0

We get rid of parentheses

15k^2+45k-11k+15=0

We add all the numbers together, and all the variables

15k^2+34k+15=0

a = 15; b = 34; c = +15;
Δ = b2-4ac
Δ = 342-4·15·15
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-16}{2*15}=\frac{-50}{30}
=-1+2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+16}{2*15}=\frac{-18}{30}
=-3/5
$