q^2-100q=4

Solution for q^2-100q=4 equation:

q^2-100q=4

We move all terms to the left:

q^2-100q-(4)=0

a = 1; b = -100; c = -4;
Δ = b2-4ac
Δ = -1002-4·1·(-4)
Δ = 10016
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:

$\sqrt{\Delta}=\sqrt{10016}=\sqrt{16*626}=\sqrt{16}*\sqrt{626}=4\sqrt{626}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{626}}{2*1}=\frac{100-4\sqrt{626}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{626}}{2*1}=\frac{100+4\sqrt{626}}{2}
$