1.5t2=53.2t

Solution for 1.5t2=53.2t equation:

1.5t^2=53.2t

We move all terms to the left:

1.5t^2-(53.2t)=0

We add all the numbers together, and all the variables

1.5t^2-(+53.2t)=0

We get rid of parentheses

1.5t^2-53.2t=0

a = 1.5; b = -53.2; c = 0;
Δ = b2-4ac
Δ = -53.22-4·1.5·0
Δ = 2830.24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53.2)-\sqrt{2830.24}}{2*1.5}=\frac{53.2-\sqrt{2830.24}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53.2)+\sqrt{2830.24}}{2*1.5}=\frac{53.2+\sqrt{2830.24}}{3}
$