7=47-4.9x^2

Solution for 7=47-4.9x^2 equation:

7=47-4.9x^2

We move all terms to the left:

7-(47-4.9x^2)=0

We get rid of parentheses

4.9x^2-47+7=0

We add all the numbers together, and all the variables

4.9x^2-40=0

a = 4.9; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·4.9·(-40)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28}{2*4.9}=\frac{-28}{9.8}
=-2+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28}{2*4.9}=\frac{28}{9.8}
=2+6/7
$