245=1/2x^2

Solution for 245=1/2x^2 equation:

245=1/2x^2

We move all terms to the left:

245-(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+245=0

We multiply all the terms by the denominator


245*2x^2-1=0

Wy multiply elements

490x^2-1=0

a = 490; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·490·(-1)
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{10}}{2*490}=\frac{0-14\sqrt{10}}{980}
=-\frac{14\sqrt{10}}{980}
=-\frac{\sqrt{10}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{10}}{2*490}=\frac{0+14\sqrt{10}}{980}
=\frac{14\sqrt{10}}{980}
=\frac{\sqrt{10}}{70}
$