1/4x-5=5x+8

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

1/4x-5=5x+8

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-20x^2-52x+1=0

a = -20; b = -52; c = +1;
Δ = b2-4ac
Δ = -522-4·(-20)·1
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{174}}{2*-20}=\frac{52-4\sqrt{174}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{174}}{2*-20}=\frac{52+4\sqrt{174}}{-40}
$