0=-0.1x2+2.4x+8.1

Solution for 0=-0.1x2+2.4x+8.1 equation:

0=-0.1x^2+2.4x+8.1

We move all terms to the left:

0-(-0.1x^2+2.4x+8.1)=0

We add all the numbers together, and all the variables

-(-0.1x^2+2.4x+8.1)=0

We get rid of parentheses

0.1x^2-2.4x-8.1=0

a = 0.1; b = -2.4; c = -8.1;
Δ = b2-4ac
Δ = -2.42-4·0.1·(-8.1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.4)-3}{2*0.1}=\frac{-0.6}{0.2}
=-2+0.2/0.2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.4)+3}{2*0.1}=\frac{5.4}{0.2}
=27
$