90t^2+60t+600=1650

Solution for 90t^2+60t+600=1650 equation:

90t^2+60t+600=1650

We move all terms to the left:

90t^2+60t+600-(1650)=0

We add all the numbers together, and all the variables

90t^2+60t-1050=0

a = 90; b = 60; c = -1050;
Δ = b2-4ac
Δ = 602-4·90·(-1050)
Δ = 381600
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:

$\sqrt{\Delta}=\sqrt{381600}=\sqrt{3600*106}=\sqrt{3600}*\sqrt{106}=60\sqrt{106}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60\sqrt{106}}{2*90}=\frac{-60-60\sqrt{106}}{180}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60\sqrt{106}}{2*90}=\frac{-60+60\sqrt{106}}{180}
$