1/3x-7=5x+7

Solution for 1/3x-7=5x+7 equation:

1/3x-7=5x+7

We move all terms to the left:

1/3x-7-(5x+7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-5x-7-7=0

We multiply all the terms by the denominator


-5x*3x-7*3x-7*3x+1=0

Wy multiply elements

-15x^2-21x-21x+1=0

We add all the numbers together, and all the variables

-15x^2-42x+1=0

a = -15; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·(-15)·1
Δ = 1824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-4\sqrt{114}}{2*-15}=\frac{42-4\sqrt{114}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+4\sqrt{114}}{2*-15}=\frac{42+4\sqrt{114}}{-30}
$