/4x-5=8+4x

Solution for /4x-5=8+4x equation:

/4x-5=8+4x

We move all terms to the left:

/4x-5-(8+4x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

/4x-(4x+8)-5=0

We get rid of parentheses

/4x-4x-8-5=0

We multiply all the terms by the denominator


-4x*4x-8*4x-5*4x+=0

We add all the numbers together, and all the variables

-4x*4x-8*4x-5*4x=0

Wy multiply elements

-16x^2-32x-20x=0

We add all the numbers together, and all the variables

-16x^2-52x=0

a = -16; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·(-16)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*-16}=\frac{0}{-32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*-16}=\frac{104}{-32}
=-3+1/4
$