2.3t+4.9t^2=41

Solution for 2.3t+4.9t^2=41 equation:

2.3t+4.9t^2=41

We move all terms to the left:

2.3t+4.9t^2-(41)=0

a = 4.9; b = 2.3; c = -41;
Δ = b2-4ac
Δ = 2.32-4·4.9·(-41)
Δ = 808.89
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{-(2.3)-\sqrt{808.89}}{2*4.9}=\frac{-2.3-\sqrt{808.89}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.3)+\sqrt{808.89}}{2*4.9}=\frac{-2.3+\sqrt{808.89}}{9.8}
$