5=6k(-3k-4)

Solution for 5=6k(-3k-4) equation:

5=6k(-3k-4)

We move all terms to the left:

5-(6k(-3k-4))=0


We calculate terms in parentheses: -(6k(-3k-4)), so:

6k(-3k-4)

We multiply parentheses

-18k^2-24k

Back to the equation:

-(-18k^2-24k)


We get rid of parentheses

18k^2+24k+5=0

a = 18; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·18·5
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{6}}{2*18}=\frac{-24-6\sqrt{6}}{36}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{6}}{2*18}=\frac{-24+6\sqrt{6}}{36}
$