8t^2+8t=72

Solution for 8t^2+8t=72 equation:

8t^2+8t=72

We move all terms to the left:

8t^2+8t-(72)=0

a = 8; b = 8; c = -72;
Δ = b2-4ac
Δ = 82-4·8·(-72)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{37}}{2*8}=\frac{-8-8\sqrt{37}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{37}}{2*8}=\frac{-8+8\sqrt{37}}{16}
$