10-q2=4q+1

Solution for 10-q2=4q+1 equation:

10-q2=4q+1

We move all terms to the left:

10-q2-(4q+1)=0

We add all the numbers together, and all the variables

-1q^2-(4q+1)+10=0

We get rid of parentheses

-1q^2-4q-1+10=0

We add all the numbers together, and all the variables

-1q^2-4q+9=0

a = -1; b = -4; c = +9;
Δ = b2-4ac
Δ = -42-4·(-1)·9
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{13}}{2*-1}=\frac{4-2\sqrt{13}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{13}}{2*-1}=\frac{4+2\sqrt{13}}{-2}
$