2x+9=56/x

Solution for 2x+9=56/x equation:

2x+9=56/x

We move all terms to the left:

2x+9-(56/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

2x-(+56/x)+9=0

We get rid of parentheses

2x-56/x+9=0

We multiply all the terms by the denominator


2x*x+9*x-56=0

We add all the numbers together, and all the variables

9x+2x*x-56=0

Wy multiply elements

2x^2+9x-56=0

a = 2; b = 9; c = -56;
Δ = b2-4ac
Δ = 92-4·2·(-56)
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{-(9)-23}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+23}{2*2}=\frac{14}{4}
=3+1/2
$