30t-t^2=155+5t

Solution for 30t-t^2=155+5t equation:

30t-t^2=155+5t

We move all terms to the left:

30t-t^2-(155+5t)=0

We add all the numbers together, and all the variables

-t^2+30t-(5t+155)=0

We add all the numbers together, and all the variables

-1t^2+30t-(5t+155)=0

We get rid of parentheses

-1t^2+30t-5t-155=0

We add all the numbers together, and all the variables

-1t^2+25t-155=0

a = -1; b = 25; c = -155;
Δ = b2-4ac
Δ = 252-4·(-1)·(-155)
Δ = 5
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{-(25)-\sqrt{5}}{2*-1}=\frac{-25-\sqrt{5}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{5}}{2*-1}=\frac{-25+\sqrt{5}}{-2}
$