(5/6)y=5/24

Solution for (5/6)y=5/24 equation:

(5/6)y=5/24

We move all terms to the left:

(5/6)y-(5/24)=0


Domain of the equation: 6)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+5/6)y-(+5/24)=0

We multiply parentheses

5y^2-(+5/24)=0

We get rid of parentheses

5y^2-5/24=0

We multiply all the terms by the denominator


5y^2*24-5=0

Wy multiply elements

120y^2-5=0

a = 120; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·120·(-5)
Δ = 2400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*120}=\frac{0-20\sqrt{6}}{240}
=-\frac{20\sqrt{6}}{240}
=-\frac{\sqrt{6}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*120}=\frac{0+20\sqrt{6}}{240}
=\frac{20\sqrt{6}}{240}
=\frac{\sqrt{6}}{12}
$