4x^2/2x-8=12

Solution for 4x^2/2x-8=12 equation:

4x^2/2x-8=12

We move all terms to the left:

4x^2/2x-8-(12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x^2/2x-20=0

We multiply all the terms by the denominator


4x^2-20*2x=0

Wy multiply elements

4x^2-40x=0

a = 4; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·4·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*4}=\frac{80}{8}
=10
$