x-4=4x-25/4x

Solution for x-4=4x-25/4x equation:

x-4=4x-25/4x

We move all terms to the left:

x-4-(4x-25/4x)=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-(+4x-25/4x)-4=0

We get rid of parentheses

x-4x+25/4x-4=0

We multiply all the terms by the denominator


x*4x-4x*4x-4*4x+25=0

Wy multiply elements

4x^2-16x^2-16x+25=0

We add all the numbers together, and all the variables

-12x^2-16x+25=0

a = -12; b = -16; c = +25;
Δ = b2-4ac
Δ = -162-4·(-12)·25
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{91}}{2*-12}=\frac{16-4\sqrt{91}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{91}}{2*-12}=\frac{16+4\sqrt{91}}{-24}
$