32t^2-5=45

Solution for 32t^2-5=45 equation:

32t^2-5=45

We move all terms to the left:

32t^2-5-(45)=0

We add all the numbers together, and all the variables

32t^2-50=0

a = 32; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·32·(-50)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*32}=\frac{-80}{64}
=-1+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*32}=\frac{80}{64}
=1+1/4
$