-2x+1/4x=50

Solution for -2x+1/4x=50 equation:

-2x+1/4x=50

We move all terms to the left:

-2x+1/4x-(50)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


-2x*4x-50*4x+1=0

Wy multiply elements

-8x^2-200x+1=0

a = -8; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·(-8)·1
Δ = 40032
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:

$\sqrt{\Delta}=\sqrt{40032}=\sqrt{144*278}=\sqrt{144}*\sqrt{278}=12\sqrt{278}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-12\sqrt{278}}{2*-8}=\frac{200-12\sqrt{278}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+12\sqrt{278}}{2*-8}=\frac{200+12\sqrt{278}}{-16}
$