1/4x=5/8x-5

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

1/4x=5/8x-5

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


8x/32x^2+(-20x)/32x^2+5=0

We multiply all the terms by the denominator


8x+(-20x)+5*32x^2=0

Wy multiply elements

160x^2+8x+(-20x)=0

We get rid of parentheses

160x^2+8x-20x=0

We add all the numbers together, and all the variables

160x^2-12x=0

a = 160; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·160·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*160}=\frac{0}{320}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*160}=\frac{24}{320}
=3/40
$