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

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

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

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2-2x+15=0

a = -3; b = -2; c = +15;
Δ = b2-4ac
Δ = -22-4·(-3)·15
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{46}}{2*-3}=\frac{2-2\sqrt{46}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{46}}{2*-3}=\frac{2+2\sqrt{46}}{-6}
$