(5/8)y-3=1/2

Solution for (5/8)y-3=1/2 equation:

(5/8)y-3=1/2

We move all terms to the left:

(5/8)y-3-(1/2)=0


Domain of the equation: 8)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+5/8)y-3-(+1/2)=0

We multiply parentheses

5y^2-3-(+1/2)=0

We get rid of parentheses

5y^2-3-1/2=0

We multiply all the terms by the denominator


5y^2*2-1-3*2=0

We add all the numbers together, and all the variables

5y^2*2-7=0

Wy multiply elements

10y^2-7=0

a = 10; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·10·(-7)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*10}=\frac{0-2\sqrt{70}}{20}
=-\frac{2\sqrt{70}}{20}
=-\frac{\sqrt{70}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*10}=\frac{0+2\sqrt{70}}{20}
=\frac{2\sqrt{70}}{20}
=\frac{\sqrt{70}}{10}
$