300=1/2*800*x^2

Solution for 300=1/2*800*x^2 equation:

300=1/2*800x^2

We move all terms to the left:

300-(1/2*800x^2)=0


Domain of the equation: 2*800x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/2*800x^2+300=0

We multiply all the terms by the denominator


300*2*800x^2-1=0

Wy multiply elements

480000x^2*8-1=0

Wy multiply elements

3840000x^2-1=0

a = 3840000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·3840000·(-1)
Δ = 15360000
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:

$\sqrt{\Delta}=\sqrt{15360000}=\sqrt{2560000*6}=\sqrt{2560000}*\sqrt{6}=1600\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1600\sqrt{6}}{2*3840000}=\frac{0-1600\sqrt{6}}{7680000}
=-\frac{1600\sqrt{6}}{7680000}
=-\frac{\sqrt{6}}{4800}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1600\sqrt{6}}{2*3840000}=\frac{0+1600\sqrt{6}}{7680000}
=\frac{1600\sqrt{6}}{7680000}
=\frac{\sqrt{6}}{4800}
$