5t=t(t-4)

Solution for 5t=t(t-4) equation:

5t=t(t-4)

We move all terms to the left:

5t-(t(t-4))=0


We calculate terms in parentheses: -(t(t-4)), so:

t(t-4)

We multiply parentheses

t^2-4t

Back to the equation:

-(t^2-4t)


We get rid of parentheses

-t^2+5t+4t=0

We add all the numbers together, and all the variables

-1t^2+9t=0

a = -1; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-1)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-1}=\frac{-18}{-2}
=+9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-1}=\frac{0}{-2}
=0
$