5/2X-12=3x+6

Solution for 5/2X-12=3x+6 equation:

5/2X-12=3X+6

We move all terms to the left:

5/2X-12-(3X+6)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

5/2X-3X-6-12=0

We multiply all the terms by the denominator


-3X*2X-6*2X-12*2X+5=0

Wy multiply elements

-6X^2-12X-24X+5=0

We add all the numbers together, and all the variables

-6X^2-36X+5=0

a = -6; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·(-6)·5
Δ = 1416
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:

$\sqrt{\Delta}=\sqrt{1416}=\sqrt{4*354}=\sqrt{4}*\sqrt{354}=2\sqrt{354}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{354}}{2*-6}=\frac{36-2\sqrt{354}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{354}}{2*-6}=\frac{36+2\sqrt{354}}{-12}
$