1/2y^2-71=22

Solution for 1/2y^2-71=22 equation:

1/2y^2-71=22

We move all terms to the left:

1/2y^2-71-(22)=0


Domain of the equation: 2y^2!=0

y^2!=0/2

y^2!=√0

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y^2-93=0

We multiply all the terms by the denominator


-93*2y^2+1=0

Wy multiply elements

-186y^2+1=0

a = -186; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-186)·1
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{186}}{2*-186}=\frac{0-2\sqrt{186}}{-372}
=-\frac{2\sqrt{186}}{-372}
=-\frac{\sqrt{186}}{-186}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{186}}{2*-186}=\frac{0+2\sqrt{186}}{-372}
=\frac{2\sqrt{186}}{-372}
=\frac{\sqrt{186}}{-186}
$