8t2-10=82

Solution for 8t2-10=82 equation:

8t^2-10=82

We move all terms to the left:

8t^2-10-(82)=0

We add all the numbers together, and all the variables

8t^2-92=0

a = 8; b = 0; c = -92;
Δ = b2-4ac
Δ = 02-4·8·(-92)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{46}}{2*8}=\frac{0-8\sqrt{46}}{16}
=-\frac{8\sqrt{46}}{16}
=-\frac{\sqrt{46}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{46}}{2*8}=\frac{0+8\sqrt{46}}{16}
=\frac{8\sqrt{46}}{16}
=\frac{\sqrt{46}}{2}
$