2x-9/5x=45

Solution for 2x-9/5x=45 equation:

2x-9/5x=45

We move all terms to the left:

2x-9/5x-(45)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


2x*5x-45*5x-9=0

Wy multiply elements

10x^2-225x-9=0

a = 10; b = -225; c = -9;
Δ = b2-4ac
Δ = -2252-4·10·(-9)
Δ = 50985
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:

$\sqrt{\Delta}=\sqrt{50985}=\sqrt{9*5665}=\sqrt{9}*\sqrt{5665}=3\sqrt{5665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-225)-3\sqrt{5665}}{2*10}=\frac{225-3\sqrt{5665}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+3\sqrt{5665}}{2*10}=\frac{225+3\sqrt{5665}}{20}
$