Y=-4.9x^2+30x-40

Solution for Y=-4.9x^2+30x-40 equation:

=-4.9Y^2+30Y-40

We move all terms to the left:

-(-4.9Y^2+30Y-40)=0

We get rid of parentheses

4.9Y^2-30Y+40=0

a = 4.9; b = -30; c = +40;
Δ = b2-4ac
Δ = -302-4·4.9·40
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{29}}{2*4.9}=\frac{30-2\sqrt{29}}{9.8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{29}}{2*4.9}=\frac{30+2\sqrt{29}}{9.8}
$