X-18=3/5x

Solution for X-18=3/5x equation:

X-18=3/5X

We move all terms to the left:

X-18-(3/5X)=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-(+3/5X)-18=0

We get rid of parentheses

X-3/5X-18=0

We multiply all the terms by the denominator


X*5X-18*5X-3=0

Wy multiply elements

5X^2-90X-3=0

a = 5; b = -90; c = -3;
Δ = b2-4ac
Δ = -902-4·5·(-3)
Δ = 8160
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:

$\sqrt{\Delta}=\sqrt{8160}=\sqrt{16*510}=\sqrt{16}*\sqrt{510}=4\sqrt{510}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{510}}{2*5}=\frac{90-4\sqrt{510}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{510}}{2*5}=\frac{90+4\sqrt{510}}{10}
$