45+9/5x=2x

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

45+9/5x=2x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+9/5x+45=0

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}
$