(7x+9/9x)-7*(9x/9x-7)=0

Solution for (7x+9/9x)-7*(9x/9x-7)=0 equation:

(7x+9/9x)-7(9x/9x-7)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 9x-7)!=0

x∈R


We add all the numbers together, and all the variables

(+7x+9/9x)-7(9x/9x-7)=0

We multiply parentheses

(+7x+9/9x)-63x+49=0

We get rid of parentheses

7x+9/9x-63x+49=0

We multiply all the terms by the denominator


7x*9x-63x*9x+49*9x+9=0

Wy multiply elements

63x^2-567x^2+441x+9=0

We add all the numbers together, and all the variables

-504x^2+441x+9=0

a = -504; b = 441; c = +9;
Δ = b2-4ac
Δ = 4412-4·(-504)·9
Δ = 212625
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:

$\sqrt{\Delta}=\sqrt{212625}=\sqrt{2025*105}=\sqrt{2025}*\sqrt{105}=45\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(441)-45\sqrt{105}}{2*-504}=\frac{-441-45\sqrt{105}}{-1008}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(441)+45\sqrt{105}}{2*-504}=\frac{-441+45\sqrt{105}}{-1008}
$