(21/24)x=25/8

Solution for (21/24)x=25/8 equation:

(21/24)x=25/8

We move all terms to the left:

(21/24)x-(25/8)=0


Domain of the equation: 24)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+21/24)x-(+25/8)=0

We multiply parentheses

21x^2-(+25/8)=0

We get rid of parentheses

21x^2-25/8=0

We multiply all the terms by the denominator


21x^2*8-25=0

Wy multiply elements

168x^2-25=0

a = 168; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·168·(-25)
Δ = 16800
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:

$\sqrt{\Delta}=\sqrt{16800}=\sqrt{400*42}=\sqrt{400}*\sqrt{42}=20\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{42}}{2*168}=\frac{0-20\sqrt{42}}{336}
=-\frac{20\sqrt{42}}{336}
=-\frac{5\sqrt{42}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{42}}{2*168}=\frac{0+20\sqrt{42}}{336}
=\frac{20\sqrt{42}}{336}
=\frac{5\sqrt{42}}{84}
$