4.9x^2+30x+0.5=30

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

4.9x^2+30x+0.5=30

We move all terms to the left:

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 = 1478.2
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{1478.2}}{2*4.9}=\frac{-30-\sqrt{1478.2}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+\sqrt{1478.2}}{2*4.9}=\frac{-30+\sqrt{1478.2}}{9.8}
$