3/2x-2=x=+8

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

3/2x-2=x=+8

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/2x-2=0

We multiply all the terms by the denominator


-1x*2x-2*2x+3=0

Wy multiply elements

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

a = -2; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-2)·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*-2}=\frac{4-2\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*-2}=\frac{4+2\sqrt{10}}{-4}
$