(5+1/4x)+x=10

Solution for (5+1/4x)+x=10 equation:

(5+1/4x)+x=10

We move all terms to the left:

(5+1/4x)+x-(10)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(1/4x+5)+x-10=0

We add all the numbers together, and all the variables

x+(1/4x+5)-10=0

We get rid of parentheses

x+1/4x+5-10=0

We multiply all the terms by the denominator


x*4x+5*4x-10*4x+1=0

Wy multiply elements

4x^2+20x-40x+1=0

We add all the numbers together, and all the variables

4x^2-20x+1=0

a = 4; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·4·1
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{6}}{2*4}=\frac{20-8\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{6}}{2*4}=\frac{20+8\sqrt{6}}{8}
$