4700=1/2x^2

Solution for 4700=1/2x^2 equation:

4700=1/2x^2

We move all terms to the left:

4700-(1/2x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/2x^2+4700=0

We multiply all the terms by the denominator


4700*2x^2-1=0

Wy multiply elements

9400x^2-1=0

a = 9400; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9400·(-1)
Δ = 37600
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:

$\sqrt{\Delta}=\sqrt{37600}=\sqrt{400*94}=\sqrt{400}*\sqrt{94}=20\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{94}}{2*9400}=\frac{0-20\sqrt{94}}{18800}
=-\frac{20\sqrt{94}}{18800}
=-\frac{\sqrt{94}}{940}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{94}}{2*9400}=\frac{0+20\sqrt{94}}{18800}
=\frac{20\sqrt{94}}{18800}
=\frac{\sqrt{94}}{940}
$