4x+9=5x+10/x

Solution for 4x+9=5x+10/x equation:

4x+9=5x+10/x

We move all terms to the left:

4x+9-(5x+10/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+5x+10/x)+9=0

We get rid of parentheses

4x-5x-10/x+9=0

We multiply all the terms by the denominator


4x*x-5x*x+9*x-10=0

We add all the numbers together, and all the variables

9x+4x*x-5x*x-10=0

Wy multiply elements

4x^2-5x^2+9x-10=0

We add all the numbers together, and all the variables

-1x^2+9x-10=0

a = -1; b = 9; c = -10;
Δ = b2-4ac
Δ = 92-4·(-1)·(-10)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{41}}{2*-1}=\frac{-9-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*-1}=\frac{-9+\sqrt{41}}{-2}
$