7x-3/3x=3

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

7x-3/3x=3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

21x^2-9x-3=0

a = 21; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·21·(-3)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{37}}{2*21}=\frac{9-3\sqrt{37}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{37}}{2*21}=\frac{9+3\sqrt{37}}{42}
$