8=1/4x+x

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

8=1/4x+x

We move all terms to the left:

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


Domain of the equation: 4x+x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x-1/4x+8=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = 32; c = -1;
Δ = b2-4ac
Δ = 322-4·(-4)·(-1)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-12\sqrt{7}}{2*-4}=\frac{-32-12\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+12\sqrt{7}}{2*-4}=\frac{-32+12\sqrt{7}}{-8}
$