1/4x+86=2x+1

Solution for 1/4x+86=2x+1 equation:

1/4x+86=2x+1

We move all terms to the left:

1/4x+86-(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+86=0

We multiply all the terms by the denominator


-2x*4x-1*4x+86*4x+1=0

Wy multiply elements

-8x^2-4x+344x+1=0

We add all the numbers together, and all the variables

-8x^2+340x+1=0

a = -8; b = 340; c = +1;
Δ = b2-4ac
Δ = 3402-4·(-8)·1
Δ = 115632
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:

$\sqrt{\Delta}=\sqrt{115632}=\sqrt{144*803}=\sqrt{144}*\sqrt{803}=12\sqrt{803}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(340)-12\sqrt{803}}{2*-8}=\frac{-340-12\sqrt{803}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(340)+12\sqrt{803}}{2*-8}=\frac{-340+12\sqrt{803}}{-16}
$