66=2x+432/x

Solution for 66=2x+432/x equation:

66=2x+432/x

We move all terms to the left:

66-(2x+432/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+432/x)+66=0

We get rid of parentheses

-2x-432/x+66=0

We multiply all the terms by the denominator


-2x*x+66*x-432=0

We add all the numbers together, and all the variables

66x-2x*x-432=0

Wy multiply elements

-2x^2+66x-432=0

a = -2; b = 66; c = -432;
Δ = b2-4ac
Δ = 662-4·(-2)·(-432)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-30}{2*-2}=\frac{-96}{-4}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+30}{2*-2}=\frac{-36}{-4}
=+9
$