5x^2=10^11

Solution for 5x^2=10^11 equation:

5x^2=10^11

We move all terms to the left:

5x^2-(10^11)=0

We add all the numbers together, and all the variables

5x^2-100000000000=0

a = 5; b = 0; c = -100000000000;
Δ = b2-4ac
Δ = 02-4·5·(-100000000000)
Δ = 2000000000000
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:

$\sqrt{\Delta}=\sqrt{2000000000000}=\sqrt{1000000000000*2}=\sqrt{1000000000000}*\sqrt{2}=1000000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000000\sqrt{2}}{2*5}=\frac{0-1000000\sqrt{2}}{10}
=-\frac{1000000\sqrt{2}}{10}
=-100000\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000000\sqrt{2}}{2*5}=\frac{0+1000000\sqrt{2}}{10}
=\frac{1000000\sqrt{2}}{10}
=100000\sqrt{2}
$