11(x)=46-4.9x^2

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

11(x)=46-4.9x^2

We move all terms to the left:

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

We get rid of parentheses

4.9x^2+11x-46=0

a = 4.9; b = 11; c = -46;
Δ = b2-4ac
Δ = 112-4·4.9·(-46)
Δ = 1022.6
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{-(11)-\sqrt{1022.6}}{2*4.9}=\frac{-11-\sqrt{1022.6}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{1022.6}}{2*4.9}=\frac{-11+\sqrt{1022.6}}{9.8}
$