5t2=-9t+19

Solution for 5t2=-9t+19 equation:

5t^2=-9t+19

We move all terms to the left:

5t^2-(-9t+19)=0

We get rid of parentheses

5t^2+9t-19=0

a = 5; b = 9; c = -19;
Δ = b2-4ac
Δ = 92-4·5·(-19)
Δ = 461
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{-(9)-\sqrt{461}}{2*5}=\frac{-9-\sqrt{461}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{461}}{2*5}=\frac{-9+\sqrt{461}}{10}
$