K+9=6k(k-11)

Solution for K+9=6k(k-11) equation:

+9=6K(K-11)

We move all terms to the left:

+9-(6K(K-11))=0


We calculate terms in parentheses: -(6K(K-11)), so:

6K(K-11)

We multiply parentheses

6K^2-66K

Back to the equation:

-(6K^2-66K)


We get rid of parentheses

-6K^2+66K+9=0

a = -6; b = 66; c = +9;
Δ = b2-4ac
Δ = 662-4·(-6)·9
Δ = 4572
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:

$\sqrt{\Delta}=\sqrt{4572}=\sqrt{36*127}=\sqrt{36}*\sqrt{127}=6\sqrt{127}$
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6\sqrt{127}}{2*-6}=\frac{-66-6\sqrt{127}}{-12}
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6\sqrt{127}}{2*-6}=\frac{-66+6\sqrt{127}}{-12}
$