(0,1x^2)+16x-205=0

Solution for (0,1x^2)+16x-205=0 equation:

(0.1x^2)+16x-205=0

We add all the numbers together, and all the variables

16x+(0.1x^2)-205=0

We get rid of parentheses

0.1x^2+16x-205=0

a = 0.1; b = 16; c = -205;
Δ = b2-4ac
Δ = 162-4·0.1·(-205)
Δ = 338
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{338}=\sqrt{169*2}=\sqrt{169}*\sqrt{2}=13\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-13\sqrt{2}}{2*0.1}=\frac{-16-13\sqrt{2}}{0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+13\sqrt{2}}{2*0.1}=\frac{-16+13\sqrt{2}}{0.2}
$