0.6k(5k-3)+18.9=1.5k(3+2k)

Solution for 0.6k(5k-3)+18.9=1.5k(3+2k) equation:

0.6k(5k-3)+18.9=1.5k(3+2k)

We move all terms to the left:

0.6k(5k-3)+18.9-(1.5k(3+2k))=0

We add all the numbers together, and all the variables

0.6k(5k-3)-(1.5k(2k+3))+18.9=0

We multiply parentheses

0k^2+0k-(1.5k(2k+3))+18.9=0


We calculate terms in parentheses: -(1.5k(2k+3)), so:

1.5k(2k+3)

We multiply parentheses

2k^2+3k

Back to the equation:

-(2k^2+3k)


We add all the numbers together, and all the variables

k^2+k-(2k^2+3k)+18.9=0

We get rid of parentheses

k^2-2k^2+k-3k+18.9=0

We add all the numbers together, and all the variables

-1k^2-2k+18.9=0

a = -1; b = -2; c = +18.9;
Δ = b2-4ac
Δ = -22-4·(-1)·18.9
Δ = 79.6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-\sqrt{79.6}}{2*-1}=\frac{2-\sqrt{79.6}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{79.6}}{2*-1}=\frac{2+\sqrt{79.6}}{-2}
$