5x-9=6/5x+9

Solution for 5x-9=6/5x+9 equation:

5x-9=6/5x+9

We move all terms to the left:

5x-9-(6/5x+9)=0


Domain of the equation: 5x+9)!=0

x∈R


We get rid of parentheses

5x-6/5x-9-9=0

We multiply all the terms by the denominator


5x*5x-9*5x-9*5x-6=0

Wy multiply elements

25x^2-45x-45x-6=0

We add all the numbers together, and all the variables

25x^2-90x-6=0

a = 25; b = -90; c = -6;
Δ = b2-4ac
Δ = -902-4·25·(-6)
Δ = 8700
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:

$\sqrt{\Delta}=\sqrt{8700}=\sqrt{100*87}=\sqrt{100}*\sqrt{87}=10\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{87}}{2*25}=\frac{90-10\sqrt{87}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{87}}{2*25}=\frac{90+10\sqrt{87}}{50}
$