500=0.1x^2+2.4x+25

Solution for 500=0.1x^2+2.4x+25 equation:

500=0.1x^2+2.4x+25

We move all terms to the left:

500-(0.1x^2+2.4x+25)=0

We get rid of parentheses

-0.1x^2-2.4x-25+500=0

We add all the numbers together, and all the variables

-0.1x^2-2.4x+475=0

a = -0.1; b = -2.4; c = +475;
Δ = b2-4ac
Δ = -2.42-4·(-0.1)·475
Δ = 195.76
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{195.76}}{2*-0.1}=\frac{2.4-\sqrt{195.76}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.4)+\sqrt{195.76}}{2*-0.1}=\frac{2.4+\sqrt{195.76}}{-0.2}
$