3x-6/2x=71

Solution for 3x-6/2x=71 equation:

3x-6/2x=71

We move all terms to the left:

3x-6/2x-(71)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-71*2x-6=0

Wy multiply elements

6x^2-142x-6=0

a = 6; b = -142; c = -6;
Δ = b2-4ac
Δ = -1422-4·6·(-6)
Δ = 20308
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:

$\sqrt{\Delta}=\sqrt{20308}=\sqrt{4*5077}=\sqrt{4}*\sqrt{5077}=2\sqrt{5077}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-142)-2\sqrt{5077}}{2*6}=\frac{142-2\sqrt{5077}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-142)+2\sqrt{5077}}{2*6}=\frac{142+2\sqrt{5077}}{12}
$