30=5t^2+8T

Solution for 30=5t^2+8T equation:

30=5t^2+8

We move all terms to the left:

30-(5t^2+8)=0

We get rid of parentheses

-5t^2-8+30=0

We add all the numbers together, and all the variables

-5t^2+22=0

a = -5; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-5)·22
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*-5}=\frac{0-2\sqrt{110}}{-10}
=-\frac{2\sqrt{110}}{-10}
=-\frac{\sqrt{110}}{-5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*-5}=\frac{0+2\sqrt{110}}{-10}
=\frac{2\sqrt{110}}{-10}
=\frac{\sqrt{110}}{-5}
$