100+50x2=8000

Solution for 100+50x2=8000 equation:

100+50x^2=8000

We move all terms to the left:

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

We add all the numbers together, and all the variables

50x^2-7900=0

a = 50; b = 0; c = -7900;
Δ = b2-4ac
Δ = 02-4·50·(-7900)
Δ = 1580000
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:

$\sqrt{\Delta}=\sqrt{1580000}=\sqrt{10000*158}=\sqrt{10000}*\sqrt{158}=100\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{158}}{2*50}=\frac{0-100\sqrt{158}}{100}
=-\frac{100\sqrt{158}}{100}
=-\sqrt{158}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{158}}{2*50}=\frac{0+100\sqrt{158}}{100}
=\frac{100\sqrt{158}}{100}
=\sqrt{158}
$