45x/x^2-36=9

Solution for 45x/x^2-36=9 equation:

45x/x^2-36=9

We move all terms to the left:

45x/x^2-36-(9)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

45x/x^2-45=0

We multiply all the terms by the denominator


45x-45*x^2=0

We add all the numbers together, and all the variables

-45x^2+45x=0

a = -45; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-45)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-45}=\frac{-90}{-90}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-45}=\frac{0}{-90}
=0
$