(2/5)x=125/8

Solution for (2/5)x=125/8 equation:

(2/5)x=125/8

We move all terms to the left:

(2/5)x-(125/8)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/5)x-(+125/8)=0

We multiply parentheses

2x^2-(+125/8)=0

We get rid of parentheses

2x^2-125/8=0

We multiply all the terms by the denominator


2x^2*8-125=0

Wy multiply elements

16x^2-125=0

a = 16; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·16·(-125)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*16}=\frac{0-40\sqrt{5}}{32}
=-\frac{40\sqrt{5}}{32}
=-\frac{5\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*16}=\frac{0+40\sqrt{5}}{32}
=\frac{40\sqrt{5}}{32}
=\frac{5\sqrt{5}}{4}
$