6=0.2t(t-7)

Solution for 6=0.2t(t-7) equation:

6=0.2t(t-7)

We move all terms to the left:

6-(0.2t(t-7))=0


We calculate terms in parentheses: -(0.2t(t-7)), so:

0.2t(t-7)

We multiply parentheses

0t^2+0t

We add all the numbers together, and all the variables

t^2+t

Back to the equation:

-(t^2+t)


We get rid of parentheses

-t^2-t+6=0

We add all the numbers together, and all the variables

-1t^2-1t+6=0

a = -1; b = -1; c = +6;
Δ = b2-4ac
Δ = -12-4·(-1)·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*-1}=\frac{-4}{-2}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-1}=\frac{6}{-2}
=-3
$