6(t-5)8t=96

Solution for 6(t-5)8t=96 equation:

6(t-5)8t=96

We move all terms to the left:

6(t-5)8t-(96)=0

We multiply parentheses

48t^2-240t-96=0

a = 48; b = -240; c = -96;
Δ = b2-4ac
Δ = -2402-4·48·(-96)
Δ = 76032
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:

$\sqrt{\Delta}=\sqrt{76032}=\sqrt{2304*33}=\sqrt{2304}*\sqrt{33}=48\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-48\sqrt{33}}{2*48}=\frac{240-48\sqrt{33}}{96}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+48\sqrt{33}}{2*48}=\frac{240+48\sqrt{33}}{96}
$