3/2x+5=6x+6/2

Solution for 3/2x+5=6x+6/2 equation:

3/2x+5=6x+6/2

We move all terms to the left:

3/2x+5-(6x+6/2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(6x+3)+5=0

We get rid of parentheses

3/2x-6x-3+5=0

We multiply all the terms by the denominator


-6x*2x-3*2x+5*2x+3=0

Wy multiply elements

-12x^2-6x+10x+3=0

We add all the numbers together, and all the variables

-12x^2+4x+3=0

a = -12; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-12)·3
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*-12}=\frac{-4-4\sqrt{10}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*-12}=\frac{-4+4\sqrt{10}}{-24}
$