24=10x+12/x

Solution for 24=10x+12/x equation:

24=10x+12/x

We move all terms to the left:

24-(10x+12/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

-(+10x+12/x)+24=0

We get rid of parentheses

-10x-12/x+24=0

We multiply all the terms by the denominator


-10x*x+24*x-12=0

We add all the numbers together, and all the variables

24x-10x*x-12=0

Wy multiply elements

-10x^2+24x-12=0

a = -10; b = 24; c = -12;
Δ = b2-4ac
Δ = 242-4·(-10)·(-12)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{6}}{2*-10}=\frac{-24-4\sqrt{6}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{6}}{2*-10}=\frac{-24+4\sqrt{6}}{-20}
$