300=1/26x2

Solution for 300=1/26x2 equation:

300=1/26x^2

We move all terms to the left:

300-(1/26x^2)=0


Domain of the equation: 26x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/26x^2+300=0

We multiply all the terms by the denominator


300*26x^2-1=0

Wy multiply elements

7800x^2-1=0

a = 7800; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·7800·(-1)
Δ = 31200
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:

$\sqrt{\Delta}=\sqrt{31200}=\sqrt{400*78}=\sqrt{400}*\sqrt{78}=20\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{78}}{2*7800}=\frac{0-20\sqrt{78}}{15600}
=-\frac{20\sqrt{78}}{15600}
=-\frac{\sqrt{78}}{780}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{78}}{2*7800}=\frac{0+20\sqrt{78}}{15600}
=\frac{20\sqrt{78}}{15600}
=\frac{\sqrt{78}}{780}
$