1/4x-4=5-2x

Solution for 1/4x-4=5-2x equation:

1/4x-4=5-2x

We move all terms to the left:

1/4x-4-(5-2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-2x+5)-4=0

We get rid of parentheses

1/4x+2x-5-4=0

We multiply all the terms by the denominator


2x*4x-5*4x-4*4x+1=0

Wy multiply elements

8x^2-20x-16x+1=0

We add all the numbers together, and all the variables

8x^2-36x+1=0

a = 8; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·8·1
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{79}}{2*8}=\frac{36-4\sqrt{79}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{79}}{2*8}=\frac{36+4\sqrt{79}}{16}
$