-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 = 11049
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{11049}}{2*6}=\frac{-105-\sqrt{11049}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11049}}{2*6}=\frac{-105+\sqrt{11049}}{12}
$