3x-14x+12=3/2x

Solution for 3x-14x+12=3/2x equation:

3x-14x+12=3/2x

We move all terms to the left:

3x-14x+12-(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

3x-14x-(+3/2x)+12=0

We add all the numbers together, and all the variables

-11x-(+3/2x)+12=0

We get rid of parentheses

-11x-3/2x+12=0

We multiply all the terms by the denominator


-11x*2x+12*2x-3=0

Wy multiply elements

-22x^2+24x-3=0

a = -22; b = 24; c = -3;
Δ = b2-4ac
Δ = 242-4·(-22)·(-3)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{78}}{2*-22}=\frac{-24-2\sqrt{78}}{-44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{78}}{2*-22}=\frac{-24+2\sqrt{78}}{-44}
$