150t-5t^2=3

Solution for 150t-5t^2=3 equation:

150t-5t^2=3

We move all terms to the left:

150t-5t^2-(3)=0

a = -5; b = 150; c = -3;
Δ = b2-4ac
Δ = 1502-4·(-5)·(-3)
Δ = 22440
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:

$\sqrt{\Delta}=\sqrt{22440}=\sqrt{4*5610}=\sqrt{4}*\sqrt{5610}=2\sqrt{5610}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{5610}}{2*-5}=\frac{-150-2\sqrt{5610}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{5610}}{2*-5}=\frac{-150+2\sqrt{5610}}{-10}
$