K=-9x^2+12x

Solution for K=-9x^2+12x equation:

=-9K^2+12K

We move all terms to the left:

-(-9K^2+12K)=0

We get rid of parentheses

9K^2-12K=0

a = 9; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·9·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*9}=\frac{0}{18}
=0
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*9}=\frac{24}{18}
=1+1/3
$