1/4x+8=2x-1

Solution for 1/4x+8=2x-1 equation:

1/4x+8=2x-1

We move all terms to the left:

1/4x+8-(2x-1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-2x+1+8=0

We multiply all the terms by the denominator


-2x*4x+1*4x+8*4x+1=0

Wy multiply elements

-8x^2+4x+32x+1=0

We add all the numbers together, and all the variables

-8x^2+36x+1=0

a = -8; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-8)·1
Δ = 1328
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:

$\sqrt{\Delta}=\sqrt{1328}=\sqrt{16*83}=\sqrt{16}*\sqrt{83}=4\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{83}}{2*-8}=\frac{-36-4\sqrt{83}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{83}}{2*-8}=\frac{-36+4\sqrt{83}}{-16}
$