15(x)=31-4.9x^2

Solution for 15(x)=31-4.9x^2 equation:

15(x)=31-4.9x^2

We move all terms to the left:

15(x)-(31-4.9x^2)=0

We get rid of parentheses

4.9x^2+15x-31=0

a = 4.9; b = 15; c = -31;
Δ = b2-4ac
Δ = 152-4·4.9·(-31)
Δ = 832.6
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{-(15)-\sqrt{832.6}}{2*4.9}=\frac{-15-\sqrt{832.6}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{832.6}}{2*4.9}=\frac{-15+\sqrt{832.6}}{9.8}
$