-38=5x+21/x

Solution for -38=5x+21/x equation:

-38=5x+21/x

We move all terms to the left:

-38-(5x+21/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

-(+5x+21/x)-38=0

We get rid of parentheses

-5x-21/x-38=0

We multiply all the terms by the denominator


-5x*x-38*x-21=0

We add all the numbers together, and all the variables

-38x-5x*x-21=0

Wy multiply elements

-5x^2-38x-21=0

a = -5; b = -38; c = -21;
Δ = b2-4ac
Δ = -382-4·(-5)·(-21)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-32}{2*-5}=\frac{6}{-10}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+32}{2*-5}=\frac{70}{-10}
=-7
$