(2x)2/(0.5-X)2=50

Solution for (2x)2/(0.5-X)2=50 equation:

(2x)2/(0.5-x)2=50

We move all terms to the left:

(2x)2/(0.5-x)2-(50)=0


Domain of the equation: (0.5-x)2!=0

x∈R


We add all the numbers together, and all the variables

2x2/(-1x+0.5)2-50=0

We multiply all the terms by the denominator


2x2-50*(-1x+0.5)2=0

We add all the numbers together, and all the variables

2x^2-50*(-1x+0.5)2=0

We multiply parentheses

2x^2+100x-50=0

a = 2; b = 100; c = -50;
Δ = b2-4ac
Δ = 1002-4·2·(-50)
Δ = 10400
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:

$\sqrt{\Delta}=\sqrt{10400}=\sqrt{400*26}=\sqrt{400}*\sqrt{26}=20\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{26}}{2*2}=\frac{-100-20\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{26}}{2*2}=\frac{-100+20\sqrt{26}}{4}
$