5t^2+1785t-18900=0

Solution for 5t^2+1785t-18900=0 equation:

5t^2+1785t-18900=0

a = 5; b = 1785; c = -18900;
Δ = b2-4ac
Δ = 17852-4·5·(-18900)
Δ = 3564225
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:

$\sqrt{\Delta}=\sqrt{3564225}=\sqrt{225*15841}=\sqrt{225}*\sqrt{15841}=15\sqrt{15841}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1785)-15\sqrt{15841}}{2*5}=\frac{-1785-15\sqrt{15841}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1785)+15\sqrt{15841}}{2*5}=\frac{-1785+15\sqrt{15841}}{10}
$