Matching
[tex]\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\quad\text{to}\quad\dfrac{15\pm\sqrt{-215}}{22}[/tex]
We can write several relationships.
... -b = 15
... 2a = 22
... b²-4ac = -215
The first of these gives b=-15; the second gives a=11. Then the third gives
... (-15)² -4·11·c = -215
... -44c = -440
... c = 10
So, the quadratic equation is 11x² -15x +10 = 0.
