-6-2/393x-14)=5/3x-4

Solution for -6-2/393x-14)=5/3x-4 equation:

-6-2/393x-14)=5/3x-4

We move all terms to the left:

-6-2/393x-14)-(5/3x-4)=0


Domain of the equation: 393x!=0

x!=0/393

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2/393x-14)-(5/3x-10)=0

We add all the numbers together, and all the variables

-2/393x-14)-(5/3x=0

We calculate fractions


(-6x)/1179x^2-(5*393x)/1179x^2+(-14)=0

We add all the numbers together, and all the variables

(-6x)/1179x^2-(+5*393x)/1179x^2+(-14)=0

We add all the numbers together, and all the variables

(-6x)/1179x^2-(+5*393x)/1179x^2-14=0

We multiply all the terms by the denominator


(-6x)-(+5*393x)-14*1179x^2=0

Wy multiply elements

-16506x^2+(-6x)-(+5*393x)=0

We get rid of parentheses

-16506x^2-6x-5*393x=0

Wy multiply elements

-16506x^2-6x-1965x=0

We add all the numbers together, and all the variables

-16506x^2-1971x=0

a = -16506; b = -1971; c = 0;
Δ = b2-4ac
Δ = -19712-4·(-16506)·0
Δ = 3884841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3884841}=1971$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1971)-1971}{2*-16506}=\frac{0}{-33012}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1971)+1971}{2*-16506}=\frac{3942}{-33012}
=-219/1834
$