1/2t^2-162=0

Solution for 1/2t^2-162=0 equation:

1/2t^2-162=0


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

t^2!=0/2

t^2!=√0

t!=0

t∈R


We multiply all the terms by the denominator


-162*2t^2+1=0

Wy multiply elements

-324t^2+1=0

a = -324; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-324)·1
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*-324}=\frac{-36}{-648}
=1/18
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*-324}=\frac{36}{-648}
=-1/18
$