0,5x+2-3/2x=1,5x-6

Solution for 0,5x+2-3/2x=1,5x-6 equation:

0.5x+2-3/2x=1.5x-6

We move all terms to the left:

0.5x+2-3/2x-(1.5x-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

0.5x-3/2x-1.5x+6+2=0

We multiply all the terms by the denominator


(0.5x)*2x-(1.5x)*2x+6*2x+2*2x-3=0

We add all the numbers together, and all the variables

(+0.5x)*2x-(+1.5x)*2x+6*2x+2*2x-3=0

We multiply parentheses

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

Wy multiply elements

0x^2-2x^2+12x+4x-3=0

We add all the numbers together, and all the variables

-1x^2+16x-3=0

a = -1; b = 16; c = -3;
Δ = b2-4ac
Δ = 162-4·(-1)·(-3)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{61}}{2*-1}=\frac{-16-2\sqrt{61}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{61}}{2*-1}=\frac{-16+2\sqrt{61}}{-2}
$