Solve a-x2 b-x c0 for x?

To solve the equation a−x2b−x=0 for x, we can multiply both sides by (b−x) to eliminate the fractions:

a−x2=0(b−x)

ab−ax−x2b+x2=0

ab−x2b−ax+x2=0

x2(1−b)+x(b−a)=ab

x2(b−1)−x(b−a)=−ab

Now we can use the quadratic formula to find the solutions for x:

x=(−b±√(b−a)2+4ab(1−b))2(1−b)

Simplifying the expression under the square root:

x=(−b±√(b−a)2+4ab−4ab2))2(1−b)

x=(−b±√(b2−2ab+a2+4ab−4ab2))2(1−b)

x=(−b±√(a2−2ab+b2))2(1−b)

x=(−b±√(a−b)2)2(1−b)

x=[−b±(a−b)]2(1−b)

x=−b±(a−b)2(1−b)

Therefore, the solutions for x are:

x1=[−b+(a−b)]2(1−b)

x2=[−b−(a−b)]2(1−b)