100=t(2+5t)

Solution for 100=t(2+5t) equation:

100=t(2+5t)

We move all terms to the left:

100-(t(2+5t))=0

We add all the numbers together, and all the variables

-(t(5t+2))+100=0


We calculate terms in parentheses: -(t(5t+2)), so:

t(5t+2)

We multiply parentheses

5t^2+2t

Back to the equation:

-(5t^2+2t)


We get rid of parentheses

-5t^2-2t+100=0

a = -5; b = -2; c = +100;
Δ = b2-4ac
Δ = -22-4·(-5)·100
Δ = 2004
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:

$\sqrt{\Delta}=\sqrt{2004}=\sqrt{4*501}=\sqrt{4}*\sqrt{501}=2\sqrt{501}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{501}}{2*-5}=\frac{2-2\sqrt{501}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{501}}{2*-5}=\frac{2+2\sqrt{501}}{-10}
$