t(0.1t-2)=30

Solution for t(0.1t-2)=30 equation:

t(0.1t-2)=30

We move all terms to the left:

t(0.1t-2)-(30)=0

We multiply parentheses

0t^2-2t-30=0

We add all the numbers together, and all the variables

t^2-2t-30=0

a = 1; b = -2; c = -30;
Δ = b2-4ac
Δ = -22-4·1·(-30)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*1}=\frac{2-2\sqrt{31}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*1}=\frac{2+2\sqrt{31}}{2}
$