6t^2-16t=10=0

Solution for 6t^2-16t=10=0 equation:

6t^2-16t=10=0

We move all terms to the left:

6t^2-16t-(10)=0

a = 6; b = -16; c = -10;
Δ = b2-4ac
Δ = -162-4·6·(-10)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{31}}{2*6}=\frac{16-4\sqrt{31}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{31}}{2*6}=\frac{16+4\sqrt{31}}{12}
$