-30=2x+72/x

Solution for -30=2x+72/x equation:

-30=2x+72/x

We move all terms to the left:

-30-(2x+72/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

-(+2x+72/x)-30=0

We get rid of parentheses

-2x-72/x-30=0

We multiply all the terms by the denominator


-2x*x-30*x-72=0

We add all the numbers together, and all the variables

-30x-2x*x-72=0

Wy multiply elements

-2x^2-30x-72=0

a = -2; b = -30; c = -72;
Δ = b2-4ac
Δ = -302-4·(-2)·(-72)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18}{2*-2}=\frac{12}{-4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18}{2*-2}=\frac{48}{-4}
=-12
$