/3x-6=7x+16

Solution for /3x-6=7x+16 equation:

/3x-6=7x+16

We move all terms to the left:

/3x-6-(7x+16)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

/3x-7x-16-6=0

We multiply all the terms by the denominator


-7x*3x-16*3x-6*3x+=0

We add all the numbers together, and all the variables

-7x*3x-16*3x-6*3x=0

Wy multiply elements

-21x^2-48x-18x=0

We add all the numbers together, and all the variables

-21x^2-66x=0

a = -21; b = -66; c = 0;
Δ = b2-4ac
Δ = -662-4·(-21)·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-66}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+66}{2*-21}=\frac{132}{-42}
=-3+1/7
$