421.5=t^2+55t

Solution for 421.5=t^2+55t equation:

421.5=t^2+55t

We move all terms to the left:

421.5-(t^2+55t)=0

We get rid of parentheses

-t^2-55t+421.5=0

We add all the numbers together, and all the variables

-1t^2-55t+421.5=0

a = -1; b = -55; c = +421.5;
Δ = b2-4ac
Δ = -552-4·(-1)·421.5
Δ = 4711
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{4711}}{2*-1}=\frac{55-\sqrt{4711}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{4711}}{2*-1}=\frac{55+\sqrt{4711}}{-2}
$