100=1/2(4x)(2x)

Solution for 100=1/2(4x)(2x) equation:

100=1/2(4x)(2x)

We move all terms to the left:

100-(1/2(4x)(2x))=0


Domain of the equation: 24x2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+1/24x2x)+100=0

We get rid of parentheses

-1/24x2x+100=0

We multiply all the terms by the denominator


100*24x2x-1=0

Wy multiply elements

2400x^2-1=0

a = 2400; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2400·(-1)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*2400}=\frac{0-40\sqrt{6}}{4800}
=-\frac{40\sqrt{6}}{4800}
=-\frac{\sqrt{6}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*2400}=\frac{0+40\sqrt{6}}{4800}
=\frac{40\sqrt{6}}{4800}
=\frac{\sqrt{6}}{120}
$