10t^2-100t-9200=0

Solution for 10t^2-100t-9200=0 equation:

10t^2-100t-9200=0

a = 10; b = -100; c = -9200;
Δ = b2-4ac
Δ = -1002-4·10·(-9200)
Δ = 378000
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:

$\sqrt{\Delta}=\sqrt{378000}=\sqrt{3600*105}=\sqrt{3600}*\sqrt{105}=60\sqrt{105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-60\sqrt{105}}{2*10}=\frac{100-60\sqrt{105}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+60\sqrt{105}}{2*10}=\frac{100+60\sqrt{105}}{20}
$