2x-10/4x+20=50

Solution for 2x-10/4x+20=50 equation:

2x-10/4x+20=50

We move all terms to the left:

2x-10/4x+20-(50)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x-10/4x-30=0

We multiply all the terms by the denominator


2x*4x-30*4x-10=0

Wy multiply elements

8x^2-120x-10=0

a = 8; b = -120; c = -10;
Δ = b2-4ac
Δ = -1202-4·8·(-10)
Δ = 14720
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:

$\sqrt{\Delta}=\sqrt{14720}=\sqrt{64*230}=\sqrt{64}*\sqrt{230}=8\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{230}}{2*8}=\frac{120-8\sqrt{230}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{230}}{2*8}=\frac{120+8\sqrt{230}}{16}
$