2+2^5/2.x=50.x

Solution for 2+2^5/2.x=50.x equation:

2+2^5/2.x=50.x

We move all terms to the left:

2+2^5/2.x-(50.x)=0


Domain of the equation: 2.x!=0

x!=0/2.

x!=0

x∈R


We add all the numbers together, and all the variables

2^5/2.x-(+50.x)+2=0

We get rid of parentheses

2^5/2.x-50.x+2=0

We multiply all the terms by the denominator


-(50.x)*2.x+2*2.x+2^5=0

We add all the numbers together, and all the variables

-(+50.x)*2.x+2*2.x+2^5=0

We add all the numbers together, and all the variables

-(+50.x)*2.x+2*2.x+32=0

We multiply parentheses

-100x^2+2*2.x+32=0

Wy multiply elements

-100x^2+4x+32=0

a = -100; b = 4; c = +32;
Δ = b2-4ac
Δ = 42-4·(-100)·32
Δ = 12816
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:

$\sqrt{\Delta}=\sqrt{12816}=\sqrt{144*89}=\sqrt{144}*\sqrt{89}=12\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12\sqrt{89}}{2*-100}=\frac{-4-12\sqrt{89}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12\sqrt{89}}{2*-100}=\frac{-4+12\sqrt{89}}{-200}
$