17=12x+4.9x^2

Solution for 17=12x+4.9x^2 equation:

17=12x+4.9x^2

We move all terms to the left:

17-(12x+4.9x^2)=0

We get rid of parentheses

-4.9x^2-12x+17=0

a = -4.9; b = -12; c = +17;
Δ = b2-4ac
Δ = -122-4·(-4.9)·17
Δ = 477.2
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{-(-12)-\sqrt{477.2}}{2*-4.9}=\frac{12-\sqrt{477.2}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+\sqrt{477.2}}{2*-4.9}=\frac{12+\sqrt{477.2}}{-9.8}
$