-1/3x+1=7x-14

Solution for -1/3x+1=7x-14 equation:

-1/3x+1=7x-14

We move all terms to the left:

-1/3x+1-(7x-14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x-7x+14+1=0

We multiply all the terms by the denominator


-7x*3x+14*3x+1*3x-1=0

Wy multiply elements

-21x^2+42x+3x-1=0

We add all the numbers together, and all the variables

-21x^2+45x-1=0

a = -21; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·(-21)·(-1)
Δ = 1941
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{-(45)-\sqrt{1941}}{2*-21}=\frac{-45-\sqrt{1941}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1941}}{2*-21}=\frac{-45+\sqrt{1941}}{-42}
$