49=1/2(x)(2x)

Solution for 49=1/2(x)(2x) equation:

49=1/2(x)(2x)

We move all terms to the left:

49-(1/2(x)(2x))=0


Domain of the equation: 2x2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+1/2x2x)+49=0

We get rid of parentheses

-1/2x2x+49=0

We multiply all the terms by the denominator


49*2x2x-1=0

Wy multiply elements

98x^2-1=0

a = 98; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·98·(-1)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*98}=\frac{0-14\sqrt{2}}{196}
=-\frac{14\sqrt{2}}{196}
=-\frac{\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*98}=\frac{0+14\sqrt{2}}{196}
=\frac{14\sqrt{2}}{196}
=\frac{\sqrt{2}}{14}
$