x/5x+9=16-2x

Solution for x/5x+9=16-2x equation:

x/5x+9=16-2x

We move all terms to the left:

x/5x+9-(16-2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x/5x-(-2x+16)+9=0

We get rid of parentheses

x/5x+2x-16+9=0

We multiply all the terms by the denominator


x+2x*5x-16*5x+9*5x=0

Wy multiply elements

10x^2+x-80x+45x=0

We add all the numbers together, and all the variables

10x^2-34x=0

a = 10; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·10·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*10}=\frac{68}{20}
=3+2/5
$