45=5t^2+50t

Solution for 45=5t^2+50t equation:

45=5t^2+50t

We move all terms to the left:

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

We get rid of parentheses

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

a = -5; b = -50; c = +45;
Δ = b2-4ac
Δ = -502-4·(-5)·45
Δ = 3400
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:

$\sqrt{\Delta}=\sqrt{3400}=\sqrt{100*34}=\sqrt{100}*\sqrt{34}=10\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{34}}{2*-5}=\frac{50-10\sqrt{34}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{34}}{2*-5}=\frac{50+10\sqrt{34}}{-10}
$