(5/6)x=24/25

Solution for (5/6)x=24/25 equation:

(5/6)x=24/25

We move all terms to the left:

(5/6)x-(24/25)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/6)x-(+24/25)=0

We multiply parentheses

5x^2-(+24/25)=0

We get rid of parentheses

5x^2-24/25=0

We multiply all the terms by the denominator


5x^2*25-24=0

Wy multiply elements

125x^2-24=0

a = 125; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·125·(-24)
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{30}}{2*125}=\frac{0-20\sqrt{30}}{250}
=-\frac{20\sqrt{30}}{250}
=-\frac{2\sqrt{30}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{30}}{2*125}=\frac{0+20\sqrt{30}}{250}
=\frac{20\sqrt{30}}{250}
=\frac{2\sqrt{30}}{25}
$