Y(2)+y(2)=288

Solution for Y(2)+y(2)=288 equation:

(2)+Y(2)=288

We move all terms to the left:

(2)+Y(2)-(288)=0

We add all the numbers together, and all the variables

Y^2-286=0

a = 1; b = 0; c = -286;
Δ = b2-4ac
Δ = 02-4·1·(-286)
Δ = 1144
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:

$\sqrt{\Delta}=\sqrt{1144}=\sqrt{4*286}=\sqrt{4}*\sqrt{286}=2\sqrt{286}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{286}}{2*1}=\frac{0-2\sqrt{286}}{2}
=-\frac{2\sqrt{286}}{2}
=-\sqrt{286}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{286}}{2*1}=\frac{0+2\sqrt{286}}{2}
=\frac{2\sqrt{286}}{2}
=\sqrt{286}
$