x-18=2/5x

Solution for x-18=2/5x equation:

x-18=2/5x

We move all terms to the left:

x-18-(2/5x)=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-(+2/5x)-18=0

We get rid of parentheses

x-2/5x-18=0

We multiply all the terms by the denominator


x*5x-18*5x-2=0

Wy multiply elements

5x^2-90x-2=0

a = 5; b = -90; c = -2;
Δ = b2-4ac
Δ = -902-4·5·(-2)
Δ = 8140
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:

$\sqrt{\Delta}=\sqrt{8140}=\sqrt{4*2035}=\sqrt{4}*\sqrt{2035}=2\sqrt{2035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2035}}{2*5}=\frac{90-2\sqrt{2035}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2035}}{2*5}=\frac{90+2\sqrt{2035}}{10}
$