7/2x-3=3x-1

Solution for 7/2x-3=3x-1 equation:

7/2x-3=3x-1

We move all terms to the left:

7/2x-3-(3x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

7/2x-3x+1-3=0

We multiply all the terms by the denominator


-3x*2x+1*2x-3*2x+7=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-6x^2-4x+7=0

a = -6; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-6)·7
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*-6}=\frac{4-2\sqrt{46}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*-6}=\frac{4+2\sqrt{46}}{-12}
$