10000+100t=800+10t^2

Solution for 10000+100t=800+10t^2 equation:

10000+100t=800+10t^2

We move all terms to the left:

10000+100t-(800+10t^2)=0

We get rid of parentheses

-10t^2+100t-800+10000=0

We add all the numbers together, and all the variables

-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}
$