4-1/3x=-7x+6

Solution for 4-1/3x=-7x+6 equation:

4-1/3x=-7x+6

We move all terms to the left:

4-1/3x-(-7x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x+7x-6+4=0

We multiply all the terms by the denominator


7x*3x-6*3x+4*3x-1=0

Wy multiply elements

21x^2-18x+12x-1=0

We add all the numbers together, and all the variables

21x^2-6x-1=0

a = 21; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·21·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{30}}{2*21}=\frac{6-2\sqrt{30}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{30}}{2*21}=\frac{6+2\sqrt{30}}{42}
$