-1/4x-5=8x+19

Solution for -1/4x-5=8x+19 equation:

-1/4x-5=8x+19

We move all terms to the left:

-1/4x-5-(8x+19)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-1/4x-8x-19-5=0

We multiply all the terms by the denominator


-8x*4x-19*4x-5*4x-1=0

Wy multiply elements

-32x^2-76x-20x-1=0

We add all the numbers together, and all the variables

-32x^2-96x-1=0

a = -32; b = -96; c = -1;
Δ = b2-4ac
Δ = -962-4·(-32)·(-1)
Δ = 9088
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:

$\sqrt{\Delta}=\sqrt{9088}=\sqrt{64*142}=\sqrt{64}*\sqrt{142}=8\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{142}}{2*-32}=\frac{96-8\sqrt{142}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{142}}{2*-32}=\frac{96+8\sqrt{142}}{-64}
$