6-5x=1/3x-7

Solution for 6-5x=1/3x-7 equation:

6-5x=1/3x-7

We move all terms to the left:

6-5x-(1/3x-7)=0


Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

-5x-1/3x+7+6=0

We multiply all the terms by the denominator


-5x*3x+7*3x+6*3x-1=0

Wy multiply elements

-15x^2+21x+18x-1=0

We add all the numbers together, and all the variables

-15x^2+39x-1=0

a = -15; b = 39; c = -1;
Δ = b2-4ac
Δ = 392-4·(-15)·(-1)
Δ = 1461
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{-(39)-\sqrt{1461}}{2*-15}=\frac{-39-\sqrt{1461}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{1461}}{2*-15}=\frac{-39+\sqrt{1461}}{-30}
$