20t=5t^2-30t+45

Solution for 20t=5t^2-30t+45 equation:

20t=5t^2-30t+45

We move all terms to the left:

20t-(5t^2-30t+45)=0

We get rid of parentheses

-5t^2+20t+30t-45=0

We add all the numbers together, and all the variables

-5t^2+50t-45=0

a = -5; b = 50; c = -45;
Δ = b2-4ac
Δ = 502-4·(-5)·(-45)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-40}{2*-5}=\frac{-90}{-10}
=+9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+40}{2*-5}=\frac{-10}{-10}
=1
$