1/2x^2+12=50

Solution for 1/2x^2+12=50 equation:

1/2x^2+12=50

We move all terms to the left:

1/2x^2+12-(50)=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^2-38=0

We multiply all the terms by the denominator


-38*2x^2+1=0

Wy multiply elements

-76x^2+1=0

a = -76; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-76)·1
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{19}}{2*-76}=\frac{0-4\sqrt{19}}{-152}
=-\frac{4\sqrt{19}}{-152}
=-\frac{\sqrt{19}}{-38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{19}}{2*-76}=\frac{0+4\sqrt{19}}{-152}
=\frac{4\sqrt{19}}{-152}
=\frac{\sqrt{19}}{-38}
$