0=50t^2+100t-90

Solution for 0=50t^2+100t-90 equation:

0=50t^2+100t-90

We move all terms to the left:

0-(50t^2+100t-90)=0

We add all the numbers together, and all the variables

-(50t^2+100t-90)=0

We get rid of parentheses

-50t^2-100t+90=0

a = -50; b = -100; c = +90;
Δ = b2-4ac
Δ = -1002-4·(-50)·90
Δ = 28000
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:

$\sqrt{\Delta}=\sqrt{28000}=\sqrt{400*70}=\sqrt{400}*\sqrt{70}=20\sqrt{70}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{70}}{2*-50}=\frac{100-20\sqrt{70}}{-100}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{70}}{2*-50}=\frac{100+20\sqrt{70}}{-100}
$