10t=-10t(t-4)

Solution for 10t=-10t(t-4) equation:

10t=-10t(t-4)

We move all terms to the left:

10t-(-10t(t-4))=0


We calculate terms in parentheses: -(-10t(t-4)), so:

-10t(t-4)

We multiply parentheses

-10t^2+40t

Back to the equation:

-(-10t^2+40t)


We get rid of parentheses

10t^2-40t+10t=0

We add all the numbers together, and all the variables

10t^2-30t=0

a = 10; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·10·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*10}=\frac{0}{20}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*10}=\frac{60}{20}
=3
$