16000+50x+0,2x^2=100000

Solution for 16000+50x+0,2x^2=100000 equation:

16000+50x+0.2x^2=100000

We move all terms to the left:

16000+50x+0.2x^2-(100000)=0

We add all the numbers together, and all the variables

0.2x^2+50x-84000=0

a = 0.2; b = 50; c = -84000;
Δ = b2-4ac
Δ = 502-4·0.2·(-84000)
Δ = 69700
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:

$\sqrt{\Delta}=\sqrt{69700}=\sqrt{100*697}=\sqrt{100}*\sqrt{697}=10\sqrt{697}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{697}}{2*0.2}=\frac{-50-10\sqrt{697}}{0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{697}}{2*0.2}=\frac{-50+10\sqrt{697}}{0.4}
$