X-18=3/7x

Solution for X-18=3/7x equation:

X-18=3/7X

We move all terms to the left:

X-18-(3/7X)=0


Domain of the equation: 7X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+3/7X)-18=0

We get rid of parentheses

X-3/7X-18=0

We multiply all the terms by the denominator


X*7X-18*7X-3=0

Wy multiply elements

7X^2-126X-3=0

a = 7; b = -126; c = -3;
Δ = b2-4ac
Δ = -1262-4·7·(-3)
Δ = 15960
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:

$\sqrt{\Delta}=\sqrt{15960}=\sqrt{4*3990}=\sqrt{4}*\sqrt{3990}=2\sqrt{3990}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3990}}{2*7}=\frac{126-2\sqrt{3990}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3990}}{2*7}=\frac{126+2\sqrt{3990}}{14}
$