30=-4.9x^2+30x+0.5

Solution for 30=-4.9x^2+30x+0.5 equation:

30=-4.9x^2+30x+0.5

We move all terms to the left:

30-(-4.9x^2+30x+0.5)=0

We get rid of parentheses

4.9x^2-30x-0.5+30=0

We add all the numbers together, and all the variables

4.9x^2-30x+29.5=0

a = 4.9; b = -30; c = +29.5;
Δ = b2-4ac
Δ = -302-4·4.9·29.5
Δ = 321.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-\sqrt{321.8}}{2*4.9}=\frac{30-\sqrt{321.8}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{321.8}}{2*4.9}=\frac{30+\sqrt{321.8}}{9.8}
$