427.75=t^2+55t

Solution for 427.75=t^2+55t equation:

427.75=t^2+55t

We move all terms to the left:

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

We get rid of parentheses

-t^2-55t+427.75=0

We add all the numbers together, and all the variables

-1t^2-55t+427.75=0

a = -1; b = -55; c = +427.75;
Δ = b2-4ac
Δ = -552-4·(-1)·427.75
Δ = 4736
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:

$\sqrt{\Delta}=\sqrt{4736}=\sqrt{64*74}=\sqrt{64}*\sqrt{74}=8\sqrt{74}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-8\sqrt{74}}{2*-1}=\frac{55-8\sqrt{74}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+8\sqrt{74}}{2*-1}=\frac{55+8\sqrt{74}}{-2}
$