9.67=x^2+x

Solution for 9.67=x^2+x equation:

9.67=x^2+x

We move all terms to the left:

9.67-(x^2+x)=0

We get rid of parentheses

-x^2-x+9.67=0

We add all the numbers together, and all the variables

-1x^2-1x+9.67=0

a = -1; b = -1; c = +9.67;
Δ = b2-4ac
Δ = -12-4·(-1)·9.67
Δ = 39.68
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{-(-1)-\sqrt{39.68}}{2*-1}=\frac{1-\sqrt{39.68}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{39.68}}{2*-1}=\frac{1+\sqrt{39.68}}{-2}
$