100000x^2=50000000

Solution for 100000x^2=50000000 equation:

100000x^2=50000000

We move all terms to the left:

100000x^2-(50000000)=0

a = 100000; b = 0; c = -50000000;
Δ = b2-4ac
Δ = 02-4·100000·(-50000000)
Δ = 20000000000000
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:

$\sqrt{\Delta}=\sqrt{20000000000000}=\sqrt{4000000000000*5}=\sqrt{4000000000000}*\sqrt{5}=2000000\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000000\sqrt{5}}{2*100000}=\frac{0-2000000\sqrt{5}}{200000}
=-\frac{2000000\sqrt{5}}{200000}
=-10\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000000\sqrt{5}}{2*100000}=\frac{0+2000000\sqrt{5}}{200000}
=\frac{2000000\sqrt{5}}{200000}
=10\sqrt{5}
$