62y^2+7=32

Solution for 62y^2+7=32 equation:

62y^2+7=32

We move all terms to the left:

62y^2+7-(32)=0

We add all the numbers together, and all the variables

62y^2-25=0

a = 62; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·62·(-25)
Δ = 6200
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:

$\sqrt{\Delta}=\sqrt{6200}=\sqrt{100*62}=\sqrt{100}*\sqrt{62}=10\sqrt{62}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{62}}{2*62}=\frac{0-10\sqrt{62}}{124}
=-\frac{10\sqrt{62}}{124}
=-\frac{5\sqrt{62}}{62}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{62}}{2*62}=\frac{0+10\sqrt{62}}{124}
=\frac{10\sqrt{62}}{124}
=\frac{5\sqrt{62}}{62}
$