O=x^2+0.19x-0.24

Solution for O=x^2+0.19x-0.24 equation:

=O^2+0.19O-0.24

We move all terms to the left:

-(O^2+0.19O-0.24)=0

We get rid of parentheses

-O^2-0.19O+0.24=0

We add all the numbers together, and all the variables

-1O^2-0.19O+0.24=0

a = -1; b = -0.19; c = +0.24;
Δ = b2-4ac
Δ = -0.192-4·(-1)·0.24
Δ = 0.9961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$O_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$O_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$O_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.19)-\sqrt{0.9961}}{2*-1}=\frac{0.19-\sqrt{0.9961}}{-2}
$
$O_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.19)+\sqrt{0.9961}}{2*-1}=\frac{0.19+\sqrt{0.9961}}{-2}
$