11=46-4.9x^2

Solution for 11=46-4.9x^2 equation:

11=46-4.9x^2

We move all terms to the left:

11-(46-4.9x^2)=0

We get rid of parentheses

4.9x^2-46+11=0

We add all the numbers together, and all the variables

4.9x^2-35=0

a = 4.9; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·4.9·(-35)
Δ = 686
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:

$\sqrt{\Delta}=\sqrt{686}=\sqrt{49*14}=\sqrt{49}*\sqrt{14}=7\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-7\sqrt{14}}{2*4.9}=\frac{0-7\sqrt{14}}{9.8}
=-\frac{7\sqrt{14}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+7\sqrt{14}}{2*4.9}=\frac{0+7\sqrt{14}}{9.8}
=\frac{7\sqrt{14}}{9.8}
$