4.9x^2=500

Solution for 4.9x^2=500 equation:

4.9x^2=500

We move all terms to the left:

4.9x^2-(500)=0

a = 4.9; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·4.9·(-500)
Δ = 9800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{2}}{2*4.9}=\frac{0-70\sqrt{2}}{9.8}
=-\frac{70\sqrt{2}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{2}}{2*4.9}=\frac{0+70\sqrt{2}}{9.8}
=\frac{70\sqrt{2}}{9.8}
$