25y^2+14=36

Solution for 25y^2+14=36 equation:

25y^2+14=36

We move all terms to the left:

25y^2+14-(36)=0

We add all the numbers together, and all the variables

25y^2-22=0

a = 25; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·25·(-22)
Δ = 2200
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:

$\sqrt{\Delta}=\sqrt{2200}=\sqrt{100*22}=\sqrt{100}*\sqrt{22}=10\sqrt{22}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{22}}{2*25}=\frac{0-10\sqrt{22}}{50}
=-\frac{10\sqrt{22}}{50}
=-\frac{\sqrt{22}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{22}}{2*25}=\frac{0+10\sqrt{22}}{50}
=\frac{10\sqrt{22}}{50}
=\frac{\sqrt{22}}{5}
$