100=1/2(25x^2)

Solution for 100=1/2(25x^2) equation:

100=1/2(25x^2)

We move all terms to the left:

100-(1/2(25x^2))=0


Domain of the equation: 225x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/225x^2+100=0

We multiply all the terms by the denominator


100*225x^2-1=0

Wy multiply elements

22500x^2-1=0

a = 22500; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·22500·(-1)
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300}{2*22500}=\frac{-300}{45000}
=-1/150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300}{2*22500}=\frac{300}{45000}
=1/150
$