-4x-3=5/x+6

Solution for -4x-3=5/x+6 equation:

-4x-3=5/x+6

We move all terms to the left:

-4x-3-(5/x+6)=0


Domain of the equation: x+6)!=0

x∈R


We get rid of parentheses

-4x-5/x-6-3=0

We multiply all the terms by the denominator


-4x*x-6*x-3*x-5=0

We add all the numbers together, and all the variables

-9x-4x*x-5=0

Wy multiply elements

-4x^2-9x-5=0

a = -4; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·(-4)·(-5)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*-4}=\frac{8}{-8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*-4}=\frac{10}{-8}
=-1+1/4
$