-4/1x+6=2/3x+28

Solution for -4/1x+6=2/3x+28 equation:

-4/1x+6=2/3x+28

We move all terms to the left:

-4/1x+6-(2/3x+28)=0


Domain of the equation: 1x!=0

x∈R



Domain of the equation: 3x+28)!=0

x∈R


We get rid of parentheses

-4/1x-2/3x-28+6=0

We calculate fractions


(-12x)/3x^2+(-2x)/3x^2-28+6=0

We add all the numbers together, and all the variables

(-12x)/3x^2+(-2x)/3x^2-22=0

We multiply all the terms by the denominator


(-12x)+(-2x)-22*3x^2=0

Wy multiply elements

-66x^2+(-12x)+(-2x)=0

We get rid of parentheses

-66x^2-12x-2x=0

We add all the numbers together, and all the variables

-66x^2-14x=0

a = -66; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-66)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-66}=\frac{0}{-132}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-66}=\frac{28}{-132}
=-7/33
$