y^2=519/20

Solution for y^2=519/20 equation:

y^2=519/20

We move all terms to the left:

y^2-(519/20)=0

We add all the numbers together, and all the variables

y^2-(+519/20)=0

We get rid of parentheses

y^2-519/20=0

We multiply all the terms by the denominator


y^2*20-519=0

Wy multiply elements

20y^2-519=0

a = 20; b = 0; c = -519;
Δ = b2-4ac
Δ = 02-4·20·(-519)
Δ = 41520
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:

$\sqrt{\Delta}=\sqrt{41520}=\sqrt{16*2595}=\sqrt{16}*\sqrt{2595}=4\sqrt{2595}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2595}}{2*20}=\frac{0-4\sqrt{2595}}{40}
=-\frac{4\sqrt{2595}}{40}
=-\frac{\sqrt{2595}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2595}}{2*20}=\frac{0+4\sqrt{2595}}{40}
=\frac{4\sqrt{2595}}{40}
=\frac{\sqrt{2595}}{10}
$