5/x-2+x=9+3x+10

Solution for 5/x-2+x=9+3x+10 equation:

5/x-2+x=9+3x+10

We move all terms to the left:

5/x-2+x-(9+3x+10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5/x+x-(3x+19)-2=0

We add all the numbers together, and all the variables

x+5/x-(3x+19)-2=0

We get rid of parentheses

x+5/x-3x-19-2=0

We multiply all the terms by the denominator


x*x-3x*x-19*x-2*x+5=0

We add all the numbers together, and all the variables

-21x+x*x-3x*x+5=0

Wy multiply elements

x^2-3x^2-21x+5=0

We add all the numbers together, and all the variables

-2x^2-21x+5=0

a = -2; b = -21; c = +5;
Δ = b2-4ac
Δ = -212-4·(-2)·5
Δ = 481
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{-(-21)-\sqrt{481}}{2*-2}=\frac{21-\sqrt{481}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{481}}{2*-2}=\frac{21+\sqrt{481}}{-4}
$