100x+50x2=8000

Solution for 100x+50x2=8000 equation:

100x+50x^2=8000

We move all terms to the left:

100x+50x^2-(8000)=0

a = 50; b = 100; c = -8000;
Δ = b2-4ac
Δ = 1002-4·50·(-8000)
Δ = 1610000
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:

$\sqrt{\Delta}=\sqrt{1610000}=\sqrt{10000*161}=\sqrt{10000}*\sqrt{161}=100\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{161}}{2*50}=\frac{-100-100\sqrt{161}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{161}}{2*50}=\frac{-100+100\sqrt{161}}{100}
$