1/3x-7=6-5x

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

1/3x-7=6-5x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2-18x-21x+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}
$