(29/5)y=187/48

Solution for (29/5)y=187/48 equation:

(29/5)y=187/48

We move all terms to the left:

(29/5)y-(187/48)=0


Domain of the equation: 5)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+29/5)y-(+187/48)=0

We multiply parentheses

29y^2-(+187/48)=0

We get rid of parentheses

29y^2-187/48=0

We multiply all the terms by the denominator


29y^2*48-187=0

Wy multiply elements

1392y^2-187=0

a = 1392; b = 0; c = -187;
Δ = b2-4ac
Δ = 02-4·1392·(-187)
Δ = 1041216
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:

$\sqrt{\Delta}=\sqrt{1041216}=\sqrt{64*16269}=\sqrt{64}*\sqrt{16269}=8\sqrt{16269}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{16269}}{2*1392}=\frac{0-8\sqrt{16269}}{2784}
=-\frac{8\sqrt{16269}}{2784}
=-\frac{\sqrt{16269}}{348}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{16269}}{2*1392}=\frac{0+8\sqrt{16269}}{2784}
=\frac{8\sqrt{16269}}{2784}
=\frac{\sqrt{16269}}{348}
$