3/(x+9)=2x-16

Solution for 3/(x+9)=2x-16 equation:

3/(x+9)=2x-16

We move all terms to the left:

3/(x+9)-(2x-16)=0


Domain of the equation: (x+9)!=0

We move all terms containing x to the left, all other terms to the right

x!=-9

x∈R


We get rid of parentheses

3/(x+9)-2x+16=0

We multiply all the terms by the denominator


-2x*(x+9)+16*(x+9)+3=0

We multiply parentheses

-2x^2-18x+16x+144+3=0

We add all the numbers together, and all the variables

-2x^2-2x+147=0

a = -2; b = -2; c = +147;
Δ = b2-4ac
Δ = -22-4·(-2)·147
Δ = 1180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{295}}{2*-2}=\frac{2-2\sqrt{295}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{295}}{2*-2}=\frac{2+2\sqrt{295}}{-4}
$