1/4x+4=5x-8

Solution for 1/4x+4=5x-8 equation:

1/4x+4=5x-8

We move all terms to the left:

1/4x+4-(5x-8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-5x+8+4=0

We multiply all the terms by the denominator


-5x*4x+8*4x+4*4x+1=0

Wy multiply elements

-20x^2+32x+16x+1=0

We add all the numbers together, and all the variables

-20x^2+48x+1=0

a = -20; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-20)·1
Δ = 2384
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:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{149}}{2*-20}=\frac{-48-4\sqrt{149}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{149}}{2*-20}=\frac{-48+4\sqrt{149}}{-40}
$