4x^2/2x-8=20

Solution for 4x^2/2x-8=20 equation:

4x^2/2x-8=20

We move all terms to the left:

4x^2/2x-8-(20)=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-28=0

We multiply all the terms by the denominator


4x^2-28*2x=0

Wy multiply elements

4x^2-56x=0

a = 4; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·4·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*4}=\frac{112}{8}
=14
$