-1/5x-8=4x+3

Solution for -1/5x-8=4x+3 equation:

-1/5x-8=4x+3

We move all terms to the left:

-1/5x-8-(4x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x-4x-3-8=0

We multiply all the terms by the denominator


-4x*5x-3*5x-8*5x-1=0

Wy multiply elements

-20x^2-15x-40x-1=0

We add all the numbers together, and all the variables

-20x^2-55x-1=0

a = -20; b = -55; c = -1;
Δ = b2-4ac
Δ = -552-4·(-20)·(-1)
Δ = 2945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{2945}}{2*-20}=\frac{55-\sqrt{2945}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{2945}}{2*-20}=\frac{55+\sqrt{2945}}{-40}
$