1/2x^2-7=74

Solution for 1/2x^2-7=74 equation:

1/2x^2-7=74

We move all terms to the left:

1/2x^2-7-(74)=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^2-81=0

We multiply all the terms by the denominator


-81*2x^2+1=0

Wy multiply elements

-162x^2+1=0

a = -162; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-162)·1
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*-162}=\frac{0-18\sqrt{2}}{-324}
=-\frac{18\sqrt{2}}{-324}
=-\frac{\sqrt{2}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*-162}=\frac{0+18\sqrt{2}}{-324}
=\frac{18\sqrt{2}}{-324}
=\frac{\sqrt{2}}{-18}
$