5/4x+16=x

Solution for 5/4x+16=x equation:

5/4x+16=x

We move all terms to the left:

5/4x+16-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5/4x+16=0

We multiply all the terms by the denominator


-1x*4x+16*4x+5=0

Wy multiply elements

-4x^2+64x+5=0

a = -4; b = 64; c = +5;
Δ = b2-4ac
Δ = 642-4·(-4)·5
Δ = 4176
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:

$\sqrt{\Delta}=\sqrt{4176}=\sqrt{144*29}=\sqrt{144}*\sqrt{29}=12\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-12\sqrt{29}}{2*-4}=\frac{-64-12\sqrt{29}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+12\sqrt{29}}{2*-4}=\frac{-64+12\sqrt{29}}{-8}
$