0.23=x^2+18.67x-27

Solution for 0.23=x^2+18.67x-27 equation:

0.23=x^2+18.67x-27

We move all terms to the left:

0.23-(x^2+18.67x-27)=0

We get rid of parentheses

-x^2-18.67x+27+0.23=0

We add all the numbers together, and all the variables

-1x^2-18.67x+27.23=0

a = -1; b = -18.67; c = +27.23;
Δ = b2-4ac
Δ = -18.672-4·(-1)·27.23
Δ = 457.4889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18.67)-\sqrt{457.4889}}{2*-1}=\frac{18.67-\sqrt{457.4889}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18.67)+\sqrt{457.4889}}{2*-1}=\frac{18.67+\sqrt{457.4889}}{-2}
$