0.05t(100+t)=50

Solution for 0.05t(100+t)=50 equation:

0.05t(100+t)=50

We move all terms to the left:

0.05t(100+t)-(50)=0

We add all the numbers together, and all the variables

0.05t(t+100)-50=0

We multiply parentheses

0t^2+0t-50=0

We add all the numbers together, and all the variables

t^2+t-50=0

a = 1; b = 1; c = -50;
Δ = b2-4ac
Δ = 12-4·1·(-50)
Δ = 201
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{-(1)-\sqrt{201}}{2*1}=\frac{-1-\sqrt{201}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{201}}{2*1}=\frac{-1+\sqrt{201}}{2}
$