K(0)=6x2-7x-3

Solution for K(0)=6x2-7x-3 equation:

(0)=6K^2-7K-3

We move all terms to the left:

(0)-(6K^2-7K-3)=0

We add all the numbers together, and all the variables

-(6K^2-7K-3)=0

We get rid of parentheses

-6K^2+7K+3=0

a = -6; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-6)·3
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-6}=\frac{4}{-12}
=-1/3
$