1/12x=-7/3x+58

Solution for 1/12x=-7/3x+58 equation:

1/12x=-7/3x+58

We move all terms to the left:

1/12x-(-7/3x+58)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 3x+58)!=0

x∈R


We get rid of parentheses

1/12x+7/3x-58=0

We calculate fractions


3x/36x^2+84x/36x^2-58=0

We multiply all the terms by the denominator


3x+84x-58*36x^2=0

We add all the numbers together, and all the variables

87x-58*36x^2=0

Wy multiply elements

-2088x^2+87x=0

a = -2088; b = 87; c = 0;
Δ = b2-4ac
Δ = 872-4·(-2088)·0
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-87}{2*-2088}=\frac{-174}{-4176}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+87}{2*-2088}=\frac{0}{-4176}
=0
$