65y^2+7=32

Solution for 65y^2+7=32 equation:

65y^2+7=32

We move all terms to the left:

65y^2+7-(32)=0

We add all the numbers together, and all the variables

65y^2-25=0

a = 65; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·65·(-25)
Δ = 6500
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:

$\sqrt{\Delta}=\sqrt{6500}=\sqrt{100*65}=\sqrt{100}*\sqrt{65}=10\sqrt{65}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{65}}{2*65}=\frac{0-10\sqrt{65}}{130}
=-\frac{10\sqrt{65}}{130}
=-\frac{\sqrt{65}}{13}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{65}}{2*65}=\frac{0+10\sqrt{65}}{130}
=\frac{10\sqrt{65}}{130}
=\frac{\sqrt{65}}{13}
$