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

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

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

We move all terms to the left:

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


Domain of the equation: 8)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

5x^2-4x+1/4=0

We multiply all the terms by the denominator


5x^2*4-4x*4+1=0

Wy multiply elements

20x^2-16x+1=0

a = 20; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·20·1
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{11}}{2*20}=\frac{16-4\sqrt{11}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{11}}{2*20}=\frac{16+4\sqrt{11}}{40}
$