7x-3=6/6x

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

7x-3=6/6x

We move all terms to the left:

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


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7x-6/6x-3=0

We multiply all the terms by the denominator


7x*6x-3*6x-6=0

Wy multiply elements

42x^2-18x-6=0

a = 42; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·42·(-6)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{37}}{2*42}=\frac{18-6\sqrt{37}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{37}}{2*42}=\frac{18+6\sqrt{37}}{84}
$