3/2x=x+12

Solution for 3/2x=x+12 equation:

3/2x=x+12

We move all terms to the left:

3/2x-(x+12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-x-12=0

We multiply all the terms by the denominator


-x*2x-12*2x+3=0

Wy multiply elements

-2x^2-24x+3=0

a = -2; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·(-2)·3
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*-2}=\frac{24-10\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*-2}=\frac{24+10\sqrt{6}}{-4}
$