1/3x-42=-2x-7

Solution for 1/3x-42=-2x-7 equation:

1/3x-42=-2x-7

We move all terms to the left:

1/3x-42-(-2x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x+2x+7-42=0

We multiply all the terms by the denominator


2x*3x+7*3x-42*3x+1=0

Wy multiply elements

6x^2+21x-126x+1=0

We add all the numbers together, and all the variables

6x^2-105x+1=0

a = 6; b = -105; c = +1;
Δ = b2-4ac
Δ = -1052-4·6·1
Δ = 11001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-\sqrt{11001}}{2*6}=\frac{105-\sqrt{11001}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11001}}{2*6}=\frac{105+\sqrt{11001}}{12}
$