4x-7/x+9=0

Solution for 4x-7/x+9=0 equation:

4x-7/x+9=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x+9*x-7=0

We add all the numbers together, and all the variables

9x+4x*x-7=0

Wy multiply elements

4x^2+9x-7=0

a = 4; b = 9; c = -7;
Δ = b2-4ac
Δ = 92-4·4·(-7)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{193}}{2*4}=\frac{-9-\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{193}}{2*4}=\frac{-9+\sqrt{193}}{8}
$