-0.1x^2+2.4x+8.1=10

Solution for -0.1x^2+2.4x+8.1=10 equation:

-0.1x^2+2.4x+8.1=10

We move all terms to the left:

-0.1x^2+2.4x+8.1-(10)=0

We add all the numbers together, and all the variables

-0.1x^2+2.4x-1.9=0

a = -0.1; b = 2.4; c = -1.9;
Δ = b2-4ac
Δ = 2.42-4·(-0.1)·(-1.9)
Δ = 5
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{-(2.4)-\sqrt{5}}{2*-0.1}=\frac{-2.4-\sqrt{5}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.4)+\sqrt{5}}{2*-0.1}=\frac{-2.4+\sqrt{5}}{-0.2}
$