16y^2+y^2=85

Solution for 16y^2+y^2=85 equation:

16y^2+y^2=85

We move all terms to the left:

16y^2+y^2-(85)=0

We add all the numbers together, and all the variables

17y^2-85=0

a = 17; b = 0; c = -85;
Δ = b2-4ac
Δ = 02-4·17·(-85)
Δ = 5780
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:

$\sqrt{\Delta}=\sqrt{5780}=\sqrt{1156*5}=\sqrt{1156}*\sqrt{5}=34\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{5}}{2*17}=\frac{0-34\sqrt{5}}{34}
=-\frac{34\sqrt{5}}{34}
=-\sqrt{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{5}}{2*17}=\frac{0+34\sqrt{5}}{34}
=\frac{34\sqrt{5}}{34}
=\sqrt{5}
$