What are the solutions to the equation x^2+ab=(a+b)x ?

The solutions to the equation x^2+ab=(a+b)x are x=a,x=b

Find the zeros of x^2+ab=(a+b)x

The zeros of x^2+ab=(a+b)x are x=a,x=b

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x^{2} + ab = (a + b) x

x = a, x = b

Solution steps

x^{2} + ab = (a + b) x

Move

(a + b) x

to the left side

x^{2} + ab - (a + b) x = 0

Write in the standard form

a x^{2} + b x + c = 0

x^{2} - (a + b) x + ab = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - a - b ) \pm ( - a - b ) ^{2} - 4 \cdot 1 \cdot ab}{2 \cdot 1}

Simplify

(- a - b)^{2} - 4 \cdot 1 \cdot ab : a - b

x_{1, 2} = \frac{- ( - a - b ) \pm ( a - b )}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - a - b ) + a - b}{2 \cdot 1}, x_{2} = \frac{- ( - a - b ) - ( a - b )}{2 \cdot 1}

x = \frac{- ( - a - b ) + a - b}{2 \cdot 1} : a

x = \frac{- ( - a - b ) - ( a - b )}{2 \cdot 1} : b

The solutions to the quadratic equation are:

x = a, x = b

6 x^{2} + 9 x - 6 = 0

4 x^{2} + 12 x + 9

z, x = \frac{3 y z ^{2}}{4}

- 3 x^{2} + 5 x - 3 = 0

4 x^{2} - 5 x = 6

What are the solutions to the equation x^2+ab=(a+b)x ?
The solutions to the equation x^2+ab=(a+b)x are x=a,x=b
Find the zeros of x^2+ab=(a+b)x
The zeros of x^2+ab=(a+b)x are x=a,x=b