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

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

100000=16000+50x+0.2x^2

We move all terms to the left:

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

We get rid of parentheses

-0.2x^2-50x-16000+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}
$