0.5x=3/2x+6

Solution for 0.5x=3/2x+6 equation:

0.5x=3/2x+6

We move all terms to the left:

0.5x-(3/2x+6)=0


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

0.5x-3/2x-6=0

We multiply all the terms by the denominator


(0.5x)*2x-6*2x-3=0

We add all the numbers together, and all the variables

(+0.5x)*2x-6*2x-3=0

We multiply parentheses

0x^2-6*2x-3=0

Wy multiply elements

0x^2-12x-3=0

We add all the numbers together, and all the variables

x^2-12x-3=0

a = 1; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·1·(-3)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*1}=\frac{12-2\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*1}=\frac{12+2\sqrt{39}}{2}
$