3/2x+8=x-4

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

3/2x+8=x-4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-x*2x+4*2x+8*2x+3=0

Wy multiply elements

-2x^2+8x+16x+3=0

We add all the numbers together, and all the variables

-2x^2+24x+3=0

a = -2; b = 24; c = +3;
Δ = b2-4ac
Δ = 242-4·(-2)·3
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*-2}=\frac{-24-10\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*-2}=\frac{-24+10\sqrt{6}}{-4}
$