(2x+32)=(1/2x+65)

Solution for (2x+32)=(1/2x+65) equation:

(2x+32)=(1/2x+65)

We move all terms to the left:

(2x+32)-((1/2x+65))=0


Domain of the equation: 2x+65))!=0

x∈R


We get rid of parentheses

2x-((1/2x+65))+32=0

We multiply all the terms by the denominator


2x*2x+32*2x+65))-((1+65))=0

We add all the numbers together, and all the variables

2x*2x+32*2x+65))-(66)=0

We add all the numbers together, and all the variables

2x*2x+32*2x=0

Wy multiply elements

4x^2+64x=0

a = 4; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·4·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*4}=\frac{-128}{8}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*4}=\frac{0}{8}
=0
$