(15/8)y+1/4=5

Solution for (15/8)y+1/4=5 equation:

(15/8)y+1/4=5

We move all terms to the left:

(15/8)y+1/4-(5)=0


Domain of the equation: 8)y!=0

y!=0/1

y!=0

y∈R


determiningTheFunctionDomain
(15/8)y-5+1/4=0

We add all the numbers together, and all the variables

(+15/8)y-5+1/4=0

We multiply parentheses

15y^2-5+1/4=0

We multiply all the terms by the denominator


15y^2*4+1-5*4=0

We add all the numbers together, and all the variables

15y^2*4-19=0

Wy multiply elements

60y^2-19=0

a = 60; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·60·(-19)
Δ = 4560
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:

$\sqrt{\Delta}=\sqrt{4560}=\sqrt{16*285}=\sqrt{16}*\sqrt{285}=4\sqrt{285}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{285}}{2*60}=\frac{0-4\sqrt{285}}{120}
=-\frac{4\sqrt{285}}{120}
=-\frac{\sqrt{285}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{285}}{2*60}=\frac{0+4\sqrt{285}}{120}
=\frac{4\sqrt{285}}{120}
=\frac{\sqrt{285}}{30}
$