X-12=3/2x-3

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

X-12=3/2X-3

We move all terms to the left:

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


Domain of the equation: 2X-3)!=0

X∈R


We get rid of parentheses

X-3/2X+3-12=0

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2+6X-24X-3=0

We add all the numbers together, and all the variables

2X^2-18X-3=0

a = 2; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·2·(-3)
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{87}}{2*2}=\frac{18-2\sqrt{87}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{87}}{2*2}=\frac{18+2\sqrt{87}}{4}
$