(3x/2)-(x+2)/4)=-8

Solution for (3x/2)-(x+2)/4)=-8 equation:

(3x/2)-(x+2)/4)=-8

We move all terms to the left:

(3x/2)-(x+2)/4)-(-8)=0

We add all the numbers together, and all the variables

(+3x/2)-(x+2)/4)-(-8)=0

We add all the numbers together, and all the variables

(+3x/2)-(x+2)/4)-(=0

We get rid of parentheses

3x/2-(x+2)/4)-(=0

We calculate fractions


12x^2/()+(-2x-4)/()=0

We multiply all the terms by the denominator


12x^2+(-2x-4)=0

We get rid of parentheses

12x^2-2x-4=0

a = 12; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·12·(-4)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*12}=\frac{16}{24}
=2/3
$