(7/3)x=7x+6

Solution for (7/3)x=7x+6 equation:

(7/3)x=7x+6

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

7x^2-(7x+6)=0

We get rid of parentheses

7x^2-7x-6=0

a = 7; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·7·(-6)
Δ = 217
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{-(-7)-\sqrt{217}}{2*7}=\frac{7-\sqrt{217}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{217}}{2*7}=\frac{7+\sqrt{217}}{14}
$