10=31-4.9x^2

Solution for 10=31-4.9x^2 equation:

10=31-4.9x^2

We move all terms to the left:

10-(31-4.9x^2)=0

We get rid of parentheses

4.9x^2-31+10=0

We add all the numbers together, and all the variables

4.9x^2-21=0

a = 4.9; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·4.9·(-21)
Δ = 411.6
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{-(0)-\sqrt{411.6}}{2*4.9}=\frac{0-\sqrt{411.6}}{9.8}
=-\frac{\sqrt{}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{411.6}}{2*4.9}=\frac{0+\sqrt{411.6}}{9.8}
=\frac{\sqrt{}}{9.8}
$