6x-5-5x+3=4(1+1/4x)

Solution for 6x-5-5x+3=4(1+1/4x) equation:

6x-5-5x+3=4(1+1/4x)

We move all terms to the left:

6x-5-5x+3-(4(1+1/4x))=0


Domain of the equation: 4x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-5x-(4(1/4x+1))-5+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


x*4x-2*4x+1))-(4(1+1))=0

We add all the numbers together, and all the variables

x*4x-2*4x+1))-(42)=0

We add all the numbers together, and all the variables

x*4x-2*4x=0

Wy multiply elements

4x^2-8x=0

a = 4; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·4·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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