3x+5=3/2x-1

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

3x+5=3/2x-1

We move all terms to the left:

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


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2+12x-3=0

a = 6; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·6·(-3)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{6}}{2*6}=\frac{-12-6\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{6}}{2*6}=\frac{-12+6\sqrt{6}}{12}
$