Y=4.9x^2-19x-53

Solution for Y=4.9x^2-19x-53 equation:

=4.9Y^2-19Y-53

We move all terms to the left:

-(4.9Y^2-19Y-53)=0

We get rid of parentheses

-4.9Y^2+19Y+53=0

a = -4.9; b = 19; c = +53;
Δ = b2-4ac
Δ = 192-4·(-4.9)·53
Δ = 1399.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{1399.8}}{2*-4.9}=\frac{-19-\sqrt{1399.8}}{-9.8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{1399.8}}{2*-4.9}=\frac{-19+\sqrt{1399.8}}{-9.8}
$