200=(10t+2)(t+8)

Solution for 200=(10t+2)(t+8) equation:

200=(10t+2)(t+8)

We move all terms to the left:

200-((10t+2)(t+8))=0

We multiply parentheses ..

-((+10t^2+80t+2t+16))+200=0


We calculate terms in parentheses: -((+10t^2+80t+2t+16)), so:

(+10t^2+80t+2t+16)

We get rid of parentheses

10t^2+80t+2t+16

We add all the numbers together, and all the variables

10t^2+82t+16

Back to the equation:

-(10t^2+82t+16)


We get rid of parentheses

-10t^2-82t-16+200=0

We add all the numbers together, and all the variables

-10t^2-82t+184=0

a = -10; b = -82; c = +184;
Δ = b2-4ac
Δ = -822-4·(-10)·184
Δ = 14084
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:

$\sqrt{\Delta}=\sqrt{14084}=\sqrt{4*3521}=\sqrt{4}*\sqrt{3521}=2\sqrt{3521}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{3521}}{2*-10}=\frac{82-2\sqrt{3521}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{3521}}{2*-10}=\frac{82+2\sqrt{3521}}{-20}
$