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 = 2628
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:

$\sqrt{\Delta}=\sqrt{2628}=\sqrt{36*73}=\sqrt{36}*\sqrt{73}=6\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{73}}{2*-9}=\frac{-42-6\sqrt{73}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{73}}{2*-9}=\frac{-42+6\sqrt{73}}{-18}
$