0,10=100+30x-0,5x^2

Solution for 0,10=100+30x-0,5x^2 equation:

0.10=100+30x-0.5x^2

We move all terms to the left:

0.10-(100+30x-0.5x^2)=0

We add all the numbers together, and all the variables

-(100+30x-0.5x^2)+0.1=0

We get rid of parentheses

0.5x^2-30x-100+0.1=0

We add all the numbers together, and all the variables

0.5x^2-30x-99.9=0

a = 0.5; b = -30; c = -99.9;
Δ = b2-4ac
Δ = -302-4·0.5·(-99.9)
Δ = 1099.8
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{-(-30)-\sqrt{1099.8}}{2*0.5}=\frac{30-\sqrt{1099.8}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{1099.8}}{2*0.5}=\frac{30+\sqrt{1099.8}}{1}
$