1/4x+8x-3=50

Solution for 1/4x+8x-3=50 equation:

1/4x+8x-3=50

We move all terms to the left:

1/4x+8x-3-(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

8x+1/4x-53=0

We multiply all the terms by the denominator


8x*4x-53*4x+1=0

Wy multiply elements

32x^2-212x+1=0

a = 32; b = -212; c = +1;
Δ = b2-4ac
Δ = -2122-4·32·1
Δ = 44816
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:

$\sqrt{\Delta}=\sqrt{44816}=\sqrt{16*2801}=\sqrt{16}*\sqrt{2801}=4\sqrt{2801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-212)-4\sqrt{2801}}{2*32}=\frac{212-4\sqrt{2801}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-212)+4\sqrt{2801}}{2*32}=\frac{212+4\sqrt{2801}}{64}
$