y(2/5)=3/20

Solution for y(2/5)=3/20 equation:

y(2/5)=3/20

We move all terms to the left:

y(2/5)-(3/20)=0

We add all the numbers together, and all the variables

y(+2/5)-(+3/20)=0

We multiply parentheses

2y^2-(+3/20)=0

We get rid of parentheses

2y^2-3/20=0

We multiply all the terms by the denominator


2y^2*20-3=0

Wy multiply elements

40y^2-3=0

a = 40; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·40·(-3)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*40}=\frac{0-4\sqrt{30}}{80}
=-\frac{4\sqrt{30}}{80}
=-\frac{\sqrt{30}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*40}=\frac{0+4\sqrt{30}}{80}
=\frac{4\sqrt{30}}{80}
=\frac{\sqrt{30}}{20}
$