x+8=9/5x

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

x+8=9/5x

We move all terms to the left:

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


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-9/5x+8=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2+40x-9=0

a = 5; b = 40; c = -9;
Δ = b2-4ac
Δ = 402-4·5·(-9)
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{445}}{2*5}=\frac{-40-2\sqrt{445}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{445}}{2*5}=\frac{-40+2\sqrt{445}}{10}
$