1/4x+4=4x+5

Solution for 1/4x+4=4x+5 equation:

1/4x+4=4x+5

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-16x^2-4x+1=0

a = -16; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·(-16)·1
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*-16}=\frac{4-4\sqrt{5}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*-16}=\frac{4+4\sqrt{5}}{-32}
$