8-1/4x=5x=

Solution for 8-1/4x=5x= equation:

8-1/4x=5x=

We move all terms to the left:

8-1/4x-(5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-5x-1/4x+8=0

We multiply all the terms by the denominator


-5x*4x+8*4x-1=0

Wy multiply elements

-20x^2+32x-1=0

a = -20; b = 32; c = -1;
Δ = b2-4ac
Δ = 322-4·(-20)·(-1)
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{59}}{2*-20}=\frac{-32-4\sqrt{59}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{59}}{2*-20}=\frac{-32+4\sqrt{59}}{-40}
$