3t2-48t=510

Solution for 3t2-48t=510 equation:

3t^2-48t=510

We move all terms to the left:

3t^2-48t-(510)=0

a = 3; b = -48; c = -510;
Δ = b2-4ac
Δ = -482-4·3·(-510)
Δ = 8424
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:

$\sqrt{\Delta}=\sqrt{8424}=\sqrt{324*26}=\sqrt{324}*\sqrt{26}=18\sqrt{26}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-18\sqrt{26}}{2*3}=\frac{48-18\sqrt{26}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+18\sqrt{26}}{2*3}=\frac{48+18\sqrt{26}}{6}
$