7x-9/x=0

Solution for 7x-9/x=0 equation:

7x-9/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


7x*x-9=0

Wy multiply elements

7x^2-9=0

a = 7; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·7·(-9)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7}}{2*7}=\frac{0-6\sqrt{7}}{14}
=-\frac{6\sqrt{7}}{14}
=-\frac{3\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*7}=\frac{0+6\sqrt{7}}{14}
=\frac{6\sqrt{7}}{14}
=\frac{3\sqrt{7}}{7}
$