6=31+-4.9x2

Solution for 6=31+-4.9x2 equation:

6=31+-4.9x^2

We move all terms to the left:

6-(31+-4.9x^2)=0

We use the square of the difference formula

-(31-4.9x^2)+6=0

We get rid of parentheses

4.9x^2-31+6=0

We add all the numbers together, and all the variables

4.9x^2-25=0

a = 4.9; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·4.9·(-25)
Δ = 490
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{490}=\sqrt{1*490}=\sqrt{1}*\sqrt{490}=1\sqrt{490}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1\sqrt{490}}{2*4.9}=\frac{0-1\sqrt{490}}{9.8}
=-\frac{1\sqrt{490}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1\sqrt{490}}{2*4.9}=\frac{0+1\sqrt{490}}{9.8}
=\frac{1\sqrt{490}}{9.8}
$