Solve the equation: `|[a,a,x],[a,a,a],[b,x,b]|=0 `

Solve the equation: x^2-x+2=0

Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a+b+c!=0.

Solve the equation -x^2+x-2=0

Find the number of real root of the equation |[0,x-a, x-b],[ x+a,0,x-c],[ x+b, x+c,0]|=0,a!=b!=c and b(a+c)> a c

Solve the equation |(x+a, x,x),(x,x+a, x),(x,x,x+a)|=0 , a!= 0

Solve the equation x^(2)-4x+[x]+3=0

Solve the following determinant equation: |[x+a, b, c], [c, x+b, a], [a ,b, x+c]|=0

Solve the equation |{:(x+a,x+b,x+c),(x+b,x+c,x+a),(x+c,x+a,x+b):}|=0

If a,b,c, in R, find the number of real root of the equation |{:(x,c,-b),(-c,x,a),(b,-a,x):}| =0

Solve the equation : (a)/(x-b)+(b)/(x-a)=2" "(xneb,a)