300=1/2*2000*x^2

Solution for 300=1/2*2000*x^2 equation:

300=1/2*2000x^2

We move all terms to the left:

300-(1/2*2000x^2)=0


Domain of the equation: 2*2000x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/2*2000x^2+300=0

We multiply all the terms by the denominator


300*2*2000x^2-1=0

Wy multiply elements

1200000x^2*2-1=0

Wy multiply elements

2400000x^2-1=0

a = 2400000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2400000·(-1)
Δ = 9600000
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:

$\sqrt{\Delta}=\sqrt{9600000}=\sqrt{640000*15}=\sqrt{640000}*\sqrt{15}=800\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{15}}{2*2400000}=\frac{0-800\sqrt{15}}{4800000}
=-\frac{800\sqrt{15}}{4800000}
=-\frac{\sqrt{15}}{6000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{15}}{2*2400000}=\frac{0+800\sqrt{15}}{4800000}
=\frac{800\sqrt{15}}{4800000}
=\frac{\sqrt{15}}{6000}
$