0.9=(0.51+4.9t)t

Solution for 0.9=(0.51+4.9t)t equation:

0.9=(0.51+4.9t)t

We move all terms to the left:

0.9-((0.51+4.9t)t)=0

We add all the numbers together, and all the variables

-((4.9t+0.51)t)+0.9=0


We calculate terms in parentheses: -((4.9t+0.51)t), so:

(4.9t+0.51)t

We multiply parentheses

4t^2+0.51t

Back to the equation:

-(4t^2+0.51t)


We get rid of parentheses

-4t^2-0.51t+0.9=0

a = -4; b = -0.51; c = +0.9;
Δ = b2-4ac
Δ = -0.512-4·(-4)·0.9
Δ = 14.6601
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{-(-0.51)-\sqrt{14.6601}}{2*-4}=\frac{0.51-\sqrt{14.6601}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.51)+\sqrt{14.6601}}{2*-4}=\frac{0.51+\sqrt{14.6601}}{-8}
$