/3x-8=5x+12

Solution for /3x-8=5x+12 equation:

/3x-8=5x+12

We move all terms to the left:

/3x-8-(5x+12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

/3x-5x-12-8=0

We multiply all the terms by the denominator


-5x*3x-12*3x-8*3x+=0

We add all the numbers together, and all the variables

-5x*3x-12*3x-8*3x=0

Wy multiply elements

-15x^2-36x-24x=0

We add all the numbers together, and all the variables

-15x^2-60x=0

a = -15; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-15)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-15}=\frac{120}{-30}
=-4
$