4x^2=10^11

Solution for 4x^2=10^11 equation:

4x^2=10^11

We move all terms to the left:

4x^2-(10^11)=0

We add all the numbers together, and all the variables

4x^2-100000000000=0

a = 4; b = 0; c = -100000000000;
Δ = b2-4ac
Δ = 02-4·4·(-100000000000)
Δ = 1600000000000
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:

$\sqrt{\Delta}=\sqrt{1600000000000}=\sqrt{160000000000*10}=\sqrt{160000000000}*\sqrt{10}=400000\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400000\sqrt{10}}{2*4}=\frac{0-400000\sqrt{10}}{8}
=-\frac{400000\sqrt{10}}{8}
=-50000\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400000\sqrt{10}}{2*4}=\frac{0+400000\sqrt{10}}{8}
=\frac{400000\sqrt{10}}{8}
=50000\sqrt{10}
$