10-q^2=2q+1

Solution for 10-q^2=2q+1 equation:

10-q^2=2q+1

We move all terms to the left:

10-q^2-(2q+1)=0

We add all the numbers together, and all the variables

-1q^2-(2q+1)+10=0

We get rid of parentheses

-1q^2-2q-1+10=0

We add all the numbers together, and all the variables

-1q^2-2q+9=0

a = -1; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-1)·9
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{10}}{2*-1}=\frac{2-2\sqrt{10}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{10}}{2*-1}=\frac{2+2\sqrt{10}}{-2}
$