4x^2=10^9

Solution for 4x^2=10^9 equation:

4x^2=10^9

We move all terms to the left:

4x^2-(10^9)=0

We add all the numbers together, and all the variables

4x^2-1000000000=0

a = 4; b = 0; c = -1000000000;
Δ = b2-4ac
Δ = 02-4·4·(-1000000000)
Δ = 16000000000
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:

$\sqrt{\Delta}=\sqrt{16000000000}=\sqrt{1600000000*10}=\sqrt{1600000000}*\sqrt{10}=40000\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40000\sqrt{10}}{2*4}=\frac{0-40000\sqrt{10}}{8}
=-\frac{40000\sqrt{10}}{8}
=-5000\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40000\sqrt{10}}{2*4}=\frac{0+40000\sqrt{10}}{8}
=\frac{40000\sqrt{10}}{8}
=5000\sqrt{10}
$