270=3k(1+k)

Solution for 270=3k(1+k) equation:

270=3k(1+k)

We move all terms to the left:

270-(3k(1+k))=0

We add all the numbers together, and all the variables

-(3k(k+1))+270=0


We calculate terms in parentheses: -(3k(k+1)), so:

3k(k+1)

We multiply parentheses

3k^2+3k

Back to the equation:

-(3k^2+3k)


We get rid of parentheses

-3k^2-3k+270=0

a = -3; b = -3; c = +270;
Δ = b2-4ac
Δ = -32-4·(-3)·270
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-57}{2*-3}=\frac{-54}{-6}
=+9
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+57}{2*-3}=\frac{60}{-6}
=-10
$