10=0.2t(t-5.1)

Solution for 10=0.2t(t-5.1) equation:

10=0.2t(t-5.1)

We move all terms to the left:

10-(0.2t(t-5.1))=0


We calculate terms in parentheses: -(0.2t(t-5.1)), so:

0.2t(t-5.1)

We multiply parentheses

0t^2-0t

We add all the numbers together, and all the variables

t^2-1t

Back to the equation:

-(t^2-1t)


We get rid of parentheses

-t^2+1t+10=0

We add all the numbers together, and all the variables

-1t^2+t+10=0

a = -1; b = 1; c = +10;
Δ = b2-4ac
Δ = 12-4·(-1)·10
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{41}}{2*-1}=\frac{-1-\sqrt{41}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*-1}=\frac{-1+\sqrt{41}}{-2}
$