3/2x-1=3x-5

Solution for 3/2x-1=3x-5 equation:

3/2x-1=3x-5

We move all terms to the left:

3/2x-1-(3x-5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-3x+5-1=0

We multiply all the terms by the denominator


-3x*2x+5*2x-1*2x+3=0

Wy multiply elements

-6x^2+10x-2x+3=0

We add all the numbers together, and all the variables

-6x^2+8x+3=0

a = -6; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-6)·3
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*-6}=\frac{-8-2\sqrt{34}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*-6}=\frac{-8+2\sqrt{34}}{-12}
$