-24/x+42=9x

Solution for -24/x+42=9x equation:

-24/x+42=9x

We move all terms to the left:

-24/x+42-(9x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-9x-24/x+42=0

We multiply all the terms by the denominator


-9x*x+42*x-24=0

We add all the numbers together, and all the variables

42x-9x*x-24=0

Wy multiply elements

-9x^2+42x-24=0

a = -9; b = 42; c = -24;
Δ = b2-4ac
Δ = 422-4·(-9)·(-24)
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{-(42)-30}{2*-9}=\frac{-72}{-18}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*-9}=\frac{-12}{-18}
=2/3
$