0=q^2-25q-100

Solution for 0=q^2-25q-100 equation:

0=q^2-25q-100

We move all terms to the left:

0-(q^2-25q-100)=0

We add all the numbers together, and all the variables

-(q^2-25q-100)=0

We get rid of parentheses

-q^2+25q+100=0

We add all the numbers together, and all the variables

-1q^2+25q+100=0

a = -1; b = 25; c = +100;
Δ = b2-4ac
Δ = 252-4·(-1)·100
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{41}}{2*-1}=\frac{-25-5\sqrt{41}}{-2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{41}}{2*-1}=\frac{-25+5\sqrt{41}}{-2}
$