3t(t+7)=16-t

Solution for 3t(t+7)=16-t equation:

3t(t+7)=16-t

We move all terms to the left:

3t(t+7)-(16-t)=0

We add all the numbers together, and all the variables

3t(t+7)-(-1t+16)=0

We multiply parentheses

3t^2+21t-(-1t+16)=0

We get rid of parentheses

3t^2+21t+1t-16=0

We add all the numbers together, and all the variables

3t^2+22t-16=0

a = 3; b = 22; c = -16;
Δ = b2-4ac
Δ = 222-4·3·(-16)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-26}{2*3}=\frac{-48}{6}
=-8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+26}{2*3}=\frac{4}{6}
=2/3
$