q^2-24q=3

Solution for q^2-24q=3 equation:

q^2-24q=3

We move all terms to the left:

q^2-24q-(3)=0

a = 1; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·1·(-3)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-14\sqrt{3}}{2*1}=\frac{24-14\sqrt{3}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+14\sqrt{3}}{2*1}=\frac{24+14\sqrt{3}}{2}
$