Question 350050
x^2=-5x+24 |put all on Lhs : +5x-24 on both side
 
x^2+5x-24=0 | use Viete's method : (x+a)(x+b)=x^2+(a+b)x+ab, here a=8, b=-3
 
 hence a+b=8-3=5, ab=8*(-3)=-24 
 
(x+8)(x-3)=0, hence x=-8, or x=3 
 
Verification : 

(-8)^2=64, -5*(-8)+24=40+24=64

3^2=9, -5*3+24=-15+24=9