5/2x-3=3x

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

5/2x-3=3x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2-6x+5=0

a = -6; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·(-6)·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*-6}=\frac{6-2\sqrt{39}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*-6}=\frac{6+2\sqrt{39}}{-12}
$