t^2-628.3185t^-1/2+500=0

Solution for t^2-628.3185t^-1/2+500=0 equation:

t^2-628.3185t^-1/2+500=0

We add all the numbers together, and all the variables

t^2-628.3185t+500-1/2=0

We multiply all the terms by the denominator


t^2*2-(628.3185t)*2-1+500*2=0

We add all the numbers together, and all the variables

t^2*2-(+628.3185t)*2-1+500*2=0

We add all the numbers together, and all the variables

t^2*2-(+628.3185t)*2+999=0

We multiply parentheses

t^2*2-1256t+999=0

Wy multiply elements

2t^2-1256t+999=0

a = 2; b = -1256; c = +999;
Δ = b2-4ac
Δ = -12562-4·2·999
Δ = 1569544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1569544}=\sqrt{4*392386}=\sqrt{4}*\sqrt{392386}=2\sqrt{392386}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1256)-2\sqrt{392386}}{2*2}=\frac{1256-2\sqrt{392386}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1256)+2\sqrt{392386}}{2*2}=\frac{1256+2\sqrt{392386}}{4}
$