1/2x^2-74=37

Solution for 1/2x^2-74=37 equation:

1/2x^2-74=37

We move all terms to the left:

1/2x^2-74-(37)=0


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

x^2!=0/2

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x^2-111=0

We multiply all the terms by the denominator


-111*2x^2+1=0

Wy multiply elements

-222x^2+1=0

a = -222; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-222)·1
Δ = 888
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{222}}{2*-222}=\frac{0-2\sqrt{222}}{-444}
=-\frac{2\sqrt{222}}{-444}
=-\frac{\sqrt{222}}{-222}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{222}}{2*-222}=\frac{0+2\sqrt{222}}{-444}
=\frac{2\sqrt{222}}{-444}
=\frac{\sqrt{222}}{-222}
$