8t(2t-18)=-12

Solution for 8t(2t-18)=-12 equation:

8t(2t-18)=-12

We move all terms to the left:

8t(2t-18)-(-12)=0

We add all the numbers together, and all the variables

8t(2t-18)+12=0

We multiply parentheses

16t^2-144t+12=0

a = 16; b = -144; c = +12;
Δ = b2-4ac
Δ = -1442-4·16·12
Δ = 19968
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19968}=\sqrt{256*78}=\sqrt{256}*\sqrt{78}=16\sqrt{78}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-16\sqrt{78}}{2*16}=\frac{144-16\sqrt{78}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+16\sqrt{78}}{2*16}=\frac{144+16\sqrt{78}}{32}
$