q^2-50q-5625=0

Solution for q^2-50q-5625=0 equation:

q^2-50q-5625=0

a = 1; b = -50; c = -5625;
Δ = b2-4ac
Δ = -502-4·1·(-5625)
Δ = 25000
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:

$\sqrt{\Delta}=\sqrt{25000}=\sqrt{2500*10}=\sqrt{2500}*\sqrt{10}=50\sqrt{10}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50\sqrt{10}}{2*1}=\frac{50-50\sqrt{10}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50\sqrt{10}}{2*1}=\frac{50+50\sqrt{10}}{2}
$