9(-6t+2=8t^2)+6t

Solution for 9(-6t+2=8t^2)+6t equation:

9(-6t+2=8t^2)+6t

We move all terms to the left:

9(-6t+2-(8t^2)+6t)=0

We multiply parentheses

-72t^2-54t+54t+18=0

We add all the numbers together, and all the variables

-72t^2+18=0

a = -72; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-72)·18
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*-72}=\frac{-72}{-144}
=1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*-72}=\frac{72}{-144}
=-1/2
$