10k(k+2)=3k-3

Solution for 10k(k+2)=3k-3 equation:

10k(k+2)=3k-3

We move all terms to the left:

10k(k+2)-(3k-3)=0

We multiply parentheses

10k^2+20k-(3k-3)=0

We get rid of parentheses

10k^2+20k-3k+3=0

We add all the numbers together, and all the variables

10k^2+17k+3=0

a = 10; b = 17; c = +3;
Δ = b2-4ac
Δ = 172-4·10·3
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-13}{2*10}=\frac{-30}{20}
=-1+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*10}=\frac{-4}{20}
=-1/5
$