20t^2+135t+3050=15000

Solution for 20t^2+135t+3050=15000 equation:

20t^2+135t+3050=15000

We move all terms to the left:

20t^2+135t+3050-(15000)=0

We add all the numbers together, and all the variables

20t^2+135t-11950=0

a = 20; b = 135; c = -11950;
Δ = b2-4ac
Δ = 1352-4·20·(-11950)
Δ = 974225
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:

$\sqrt{\Delta}=\sqrt{974225}=\sqrt{25*38969}=\sqrt{25}*\sqrt{38969}=5\sqrt{38969}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-5\sqrt{38969}}{2*20}=\frac{-135-5\sqrt{38969}}{40}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+5\sqrt{38969}}{2*20}=\frac{-135+5\sqrt{38969}}{40}
$