-4(x)=11+4/x

Solution for -4(x)=11+4/x equation:

-4(x)=11+4/x

We move all terms to the left:

-4(x)-(11+4/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-(4/x+11)=0

We get rid of parentheses

-4x-4/x-11=0

We multiply all the terms by the denominator


-4x*x-11*x-4=0

We add all the numbers together, and all the variables

-11x-4x*x-4=0

Wy multiply elements

-4x^2-11x-4=0

a = -4; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·(-4)·(-4)
Δ = 57
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{-(-11)-\sqrt{57}}{2*-4}=\frac{11-\sqrt{57}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{57}}{2*-4}=\frac{11+\sqrt{57}}{-8}
$