Eavaluating the roots of quadratic equation If $b>a , c>0$ 
Determine the intervals that the roots of the equation
$(x-a)(x-b) -c =0$ belong to 
My work is to get the values of the roots in terms of a , b and c using the general form but i couldn't determine those intervals 

The given equation is $x^2-(a+b)x+ab-c=0$. But $$\Delta=(a+b)^2-4(ab-c)=(a-b)^2+4c>0.$$ So the equation has two distinct real roots. The two roots are $\frac{(a+b)+\sqrt{(a-b)^2+4c}}{2}$ and $\frac{(a+b)-\sqrt{(a-b)^2+4c}}{2}$. Hence the roots are in the interval $[\frac{(a+b)-\sqrt{(a-b)^2+4c}}{2},\frac{(a+b)+\sqrt{(a-b)^2+4c}}{2}]$.  
