(8/125)x=25/4

Solution for (8/125)x=25/4 equation:

(8/125)x=25/4

We move all terms to the left:

(8/125)x-(25/4)=0


Domain of the equation: 125)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/125)x-(+25/4)=0

We multiply parentheses

8x^2-(+25/4)=0

We get rid of parentheses

8x^2-25/4=0

We multiply all the terms by the denominator


8x^2*4-25=0

Wy multiply elements

32x^2-25=0

a = 32; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·32·(-25)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*32}=\frac{0-40\sqrt{2}}{64}
=-\frac{40\sqrt{2}}{64}
=-\frac{5\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*32}=\frac{0+40\sqrt{2}}{64}
=\frac{40\sqrt{2}}{64}
=\frac{5\sqrt{2}}{8}
$