/5x-6=3x+18

Solution for /5x-6=3x+18 equation:

/5x-6=3x+18

We move all terms to the left:

/5x-6-(3x+18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

/5x-3x-18-6=0

We multiply all the terms by the denominator


-3x*5x-18*5x-6*5x+=0

We add all the numbers together, and all the variables

-3x*5x-18*5x-6*5x=0

Wy multiply elements

-15x^2-90x-30x=0

We add all the numbers together, and all the variables

-15x^2-120x=0

a = -15; b = -120; c = 0;
Δ = b2-4ac
Δ = -1202-4·(-15)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120}{2*-15}=\frac{240}{-30}
=-8
$