9t-2t(t+8)=5t

Solution for 9t-2t(t+8)=5t equation:

9t-2t(t+8)=5t

We move all terms to the left:

9t-2t(t+8)-(5t)=0

We add all the numbers together, and all the variables

4t-2t(t+8)=0

We multiply parentheses

-2t^2+4t-16t=0

We add all the numbers together, and all the variables

-2t^2-12t=0

a = -2; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-2)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-2}=\frac{0}{-4}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-2}=\frac{24}{-4}
=-6
$