55=15x+4.9x^2

Solution for 55=15x+4.9x^2 equation:

55=15x+4.9x^2

We move all terms to the left:

55-(15x+4.9x^2)=0

We get rid of parentheses

-4.9x^2-15x+55=0

a = -4.9; b = -15; c = +55;
Δ = b2-4ac
Δ = -152-4·(-4.9)·55
Δ = 1303
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{-(-15)-\sqrt{1303}}{2*-4.9}=\frac{15-\sqrt{1303}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1303}}{2*-4.9}=\frac{15+\sqrt{1303}}{-9.8}
$