45/x+9=2x-4

Solution for 45/x+9=2x-4 equation:

45/x+9=2x-4

We move all terms to the left:

45/x+9-(2x-4)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

45/x-2x+4+9=0

We multiply all the terms by the denominator


-2x*x+4*x+9*x+45=0

We add all the numbers together, and all the variables

13x-2x*x+45=0

Wy multiply elements

-2x^2+13x+45=0

a = -2; b = 13; c = +45;
Δ = b2-4ac
Δ = 132-4·(-2)·45
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-23}{2*-2}=\frac{-36}{-4}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+23}{2*-2}=\frac{10}{-4}
=-2+1/2
$