0.215t^2=3t+4.5

Solution for 0.215t^2=3t+4.5 equation:

0.215t^2=3t+4.5

We move all terms to the left:

0.215t^2-(3t+4.5)=0

We get rid of parentheses

0.215t^2-3t-4.5=0

a = 0.215; b = -3; c = -4.5;
Δ = b2-4ac
Δ = -32-4·0.215·(-4.5)
Δ = 12.87
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{-(-3)-\sqrt{12.87}}{2*0.215}=\frac{3-\sqrt{12.87}}{0.43}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{12.87}}{2*0.215}=\frac{3+\sqrt{12.87}}{0.43}
$