1/4x+1=8x+13

Solution for 1/4x+1=8x+13 equation:

1/4x+1=8x+13

We move all terms to the left:

1/4x+1-(8x+13)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-8x-13+1=0

We multiply all the terms by the denominator


-8x*4x-13*4x+1*4x+1=0

Wy multiply elements

-32x^2-52x+4x+1=0

We add all the numbers together, and all the variables

-32x^2-48x+1=0

a = -32; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·(-32)·1
Δ = 2432
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:

$\sqrt{\Delta}=\sqrt{2432}=\sqrt{64*38}=\sqrt{64}*\sqrt{38}=8\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{38}}{2*-32}=\frac{48-8\sqrt{38}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{38}}{2*-32}=\frac{48+8\sqrt{38}}{-64}
$