K-1=5x^2+3x-6

Solution for K-1=5x^2+3x-6 equation:

-1=5K^2+3K-6

We move all terms to the left:

-1-(5K^2+3K-6)=0

We get rid of parentheses

-5K^2-3K+6-1=0

We add all the numbers together, and all the variables

-5K^2-3K+5=0

a = -5; b = -3; c = +5;
Δ = b2-4ac
Δ = -32-4·(-5)·5
Δ = 109
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{-(-3)-\sqrt{109}}{2*-5}=\frac{3-\sqrt{109}}{-10}
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{109}}{2*-5}=\frac{3+\sqrt{109}}{-10}
$