1/3x+7=2x-1

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

1/3x+7=2x-1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+3x+21x+1=0

We add all the numbers together, and all the variables

-6x^2+24x+1=0

a = -6; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-6)·1
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*-6}=\frac{-24-10\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*-6}=\frac{-24+10\sqrt{6}}{-12}
$