7x-3/3x=2

Solution for 7x-3/3x=2 equation:

7x-3/3x=2

We move all terms to the left:

7x-3/3x-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


7x*3x-2*3x-3=0

Wy multiply elements

21x^2-6x-3=0

a = 21; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·21·(-3)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{2}}{2*21}=\frac{6-12\sqrt{2}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{2}}{2*21}=\frac{6+12\sqrt{2}}{42}
$