12-x=3/2x=2

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

12-x=3/2x=2

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x-(+3/2x)+12=0

We get rid of parentheses

-1x-3/2x+12=0

We multiply all the terms by the denominator


-1x*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 = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{138}}{2*-2}=\frac{-24-2\sqrt{138}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{138}}{2*-2}=\frac{-24+2\sqrt{138}}{-4}
$