900x^2+8=200

Solution for 900x^2+8=200 equation:

900x^2+8=200

We move all terms to the left:

900x^2+8-(200)=0

We add all the numbers together, and all the variables

900x^2-192=0

a = 900; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·900·(-192)
Δ = 691200
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:

$\sqrt{\Delta}=\sqrt{691200}=\sqrt{230400*3}=\sqrt{230400}*\sqrt{3}=480\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-480\sqrt{3}}{2*900}=\frac{0-480\sqrt{3}}{1800}
=-\frac{480\sqrt{3}}{1800}
=-\frac{4\sqrt{3}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+480\sqrt{3}}{2*900}=\frac{0+480\sqrt{3}}{1800}
=\frac{480\sqrt{3}}{1800}
=\frac{4\sqrt{3}}{15}
$