90=6t^2-48t

Solution for 90=6t^2-48t equation:

90=6t^2-48t

We move all terms to the left:

90-(6t^2-48t)=0

We get rid of parentheses

-6t^2+48t+90=0

a = -6; b = 48; c = +90;
Δ = b2-4ac
Δ = 482-4·(-6)·90
Δ = 4464
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:

$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{31}}{2*-6}=\frac{-48-12\sqrt{31}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{31}}{2*-6}=\frac{-48+12\sqrt{31}}{-12}
$