3x=3/2x+5

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

3x=3/2x+5

We move all terms to the left:

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


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

3x-3/2x-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-10x-3=0

a = 6; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·6·(-3)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{43}}{2*6}=\frac{10-2\sqrt{43}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{43}}{2*6}=\frac{10+2\sqrt{43}}{12}
$