(-18t^2+90t+1800)/(t^2+5*t+100)^2=0

Solution for (-18t^2+90t+1800)/(t^2+5*t+100)^2=0 equation:

(-18t^2+90t+1800)/(t^2+5t+100)^2=0


Domain of the equation: (t^2+5t+100)^2!=0

t∈R


We multiply all the terms by the denominator


(-18t^2+90t+1800)=0

We get rid of parentheses

-18t^2+90t+1800=0

a = -18; b = 90; c = +1800;
Δ = b2-4ac
Δ = 902-4·(-18)·1800
Δ = 137700
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:

$\sqrt{\Delta}=\sqrt{137700}=\sqrt{8100*17}=\sqrt{8100}*\sqrt{17}=90\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90\sqrt{17}}{2*-18}=\frac{-90-90\sqrt{17}}{-36}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90\sqrt{17}}{2*-18}=\frac{-90+90\sqrt{17}}{-36}
$