9/x+8=2x+5

Solution for 9/x+8=2x+5 equation:

9/x+8=2x+5

We move all terms to the left:

9/x+8-(2x+5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

9/x-2x-5+8=0

We multiply all the terms by the denominator


-2x*x-5*x+8*x+9=0

We add all the numbers together, and all the variables

3x-2x*x+9=0

Wy multiply elements

-2x^2+3x+9=0

a = -2; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-2)·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-2}=\frac{6}{-4}
=-1+1/2
$