9x-3/x=78

Solution for 9x-3/x=78 equation:

9x-3/x=78

We move all terms to the left:

9x-3/x-(78)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


9x*x-78*x-3=0

We add all the numbers together, and all the variables

-78x+9x*x-3=0

Wy multiply elements

9x^2-78x-3=0

a = 9; b = -78; c = -3;
Δ = b2-4ac
Δ = -782-4·9·(-3)
Δ = 6192
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:

$\sqrt{\Delta}=\sqrt{6192}=\sqrt{144*43}=\sqrt{144}*\sqrt{43}=12\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-12\sqrt{43}}{2*9}=\frac{78-12\sqrt{43}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+12\sqrt{43}}{2*9}=\frac{78+12\sqrt{43}}{18}
$