1/2x^2+3=75

Solution for 1/2x^2+3=75 equation:

1/2x^2+3=75

We move all terms to the left:

1/2x^2+3-(75)=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^2-72=0

We multiply all the terms by the denominator


-72*2x^2+1=0

Wy multiply elements

-144x^2+1=0

a = -144; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-144)·1
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-144}=\frac{-24}{-288}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-144}=\frac{24}{-288}
=-1/12
$