-8/5x-6=-84/3x

Solution for -8/5x-6=-84/3x equation:

-8/5x-6=-84/3x

We move all terms to the left:

-8/5x-6-(-84/3x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-8/5x+84/3x-6=0

We calculate fractions


(-24x)/15x^2+420x/15x^2-6=0

We multiply all the terms by the denominator


(-24x)+420x-6*15x^2=0

We add all the numbers together, and all the variables

420x+(-24x)-6*15x^2=0

Wy multiply elements

-90x^2+420x+(-24x)=0

We get rid of parentheses

-90x^2+420x-24x=0

We add all the numbers together, and all the variables

-90x^2+396x=0

a = -90; b = 396; c = 0;
Δ = b2-4ac
Δ = 3962-4·(-90)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(396)-396}{2*-90}=\frac{-792}{-180}
=4+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(396)+396}{2*-90}=\frac{0}{-180}
=0
$