10=x+1/4x

Solution for 10=x+1/4x equation:

10=x+1/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+1/4x)+10=0

We get rid of parentheses

-x-1/4x+10=0

We multiply all the terms by the denominator


-x*4x+10*4x-1=0

Wy multiply elements

-4x^2+40x-1=0

a = -4; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·(-4)·(-1)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-12\sqrt{11}}{2*-4}=\frac{-40-12\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+12\sqrt{11}}{2*-4}=\frac{-40+12\sqrt{11}}{-8}
$