-1.031=-0.344x-4.9x^2

Solution for -1.031=-0.344x-4.9x^2 equation:

-1.031=-0.344x-4.9x^2

We move all terms to the left:

-1.031-(-0.344x-4.9x^2)=0

We get rid of parentheses

4.9x^2+0.344x-1.031=0

a = 4.9; b = 0.344; c = -1.031;
Δ = b2-4ac
Δ = 0.3442-4·4.9·(-1.031)
Δ = 20.325936
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{-(0.344)-\sqrt{20.325936}}{2*4.9}=\frac{-0.344-\sqrt{20.325936}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.344)+\sqrt{20.325936}}{2*4.9}=\frac{-0.344+\sqrt{20.325936}}{9.8}
$