2(x-5)=4+1/4x

Solution for 2(x-5)=4+1/4x equation:

2(x-5)=4+1/4x

We move all terms to the left:

2(x-5)-(4+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

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

We multiply parentheses

2x-(1/4x+4)-10=0

We get rid of parentheses

2x-1/4x-4-10=0

We multiply all the terms by the denominator


2x*4x-4*4x-10*4x-1=0

Wy multiply elements

8x^2-16x-40x-1=0

We add all the numbers together, and all the variables

8x^2-56x-1=0

a = 8; b = -56; c = -1;
Δ = b2-4ac
Δ = -562-4·8·(-1)
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-12\sqrt{22}}{2*8}=\frac{56-12\sqrt{22}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+12\sqrt{22}}{2*8}=\frac{56+12\sqrt{22}}{16}
$