2x^2=10^11

Solution for 2x^2=10^11 equation:

2x^2=10^11

We move all terms to the left:

2x^2-(10^11)=0

We add all the numbers together, and all the variables

2x^2-100000000000=0

a = 2; b = 0; c = -100000000000;
Δ = b2-4ac
Δ = 02-4·2·(-100000000000)
Δ = 800000000000
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:

$\sqrt{\Delta}=\sqrt{800000000000}=\sqrt{160000000000*5}=\sqrt{160000000000}*\sqrt{5}=400000\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400000\sqrt{5}}{2*2}=\frac{0-400000\sqrt{5}}{4}
=-\frac{400000\sqrt{5}}{4}
=-100000\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400000\sqrt{5}}{2*2}=\frac{0+400000\sqrt{5}}{4}
=\frac{400000\sqrt{5}}{4}
=100000\sqrt{5}
$