100*x^2-300=x

Solution for 100*x^2-300=x equation:

100x^2-300=x

We move all terms to the left:

100x^2-300-(x)=0

We add all the numbers together, and all the variables

100x^2-1x-300=0

a = 100; b = -1; c = -300;
Δ = b2-4ac
Δ = -12-4·100·(-300)
Δ = 120001
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:

$\sqrt{\Delta}=\sqrt{120001}=\sqrt{49*2449}=\sqrt{49}*\sqrt{2449}=7\sqrt{2449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7\sqrt{2449}}{2*100}=\frac{1-7\sqrt{2449}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7\sqrt{2449}}{2*100}=\frac{1+7\sqrt{2449}}{200}
$