What are the solutions to the equation solvefor A,B=A^2-3A+21 ?

The solutions to the equation solvefor A,B=A^2-3A+21 are A=(3+sqrt(4B-75))/2 ,A=(3-sqrt(4B-75))/2

Find the zeros of solvefor A,B=A^2-3A+21

The zeros of solvefor A,B=A^2-3A+21 are A=(3+sqrt(4B-75))/2 ,A=(3-sqrt(4B-75))/2

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solve for

A, B = A^{2} - 3 A + 21

A = \frac{3 + 4 B - 75}{2}, A = \frac{3 - 4 B - 75}{2}

Solution steps

B = A^{2} - 3 A + 21

Switch sides

A^{2} - 3 A + 21 = B

Move

B

to the left side

A^{2} - 3 A + 21 - B = 0

Solve with the quadratic formula

A_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot ( 21 - B )}{2 \cdot 1}

Simplify

(- 3)^{2} - 4 \cdot 1 \cdot (21 - B) : 4 B - 75

A_{1, 2} = \frac{- ( - 3 ) \pm 4 B - 75}{2 \cdot 1}

Separate the solutions

A_{1} = \frac{- ( - 3 ) + 4 B - 75}{2 \cdot 1}, A_{2} = \frac{- ( - 3 ) - 4 B - 75}{2 \cdot 1}

A = \frac{- ( - 3 ) + 4 B - 75}{2 \cdot 1} : \frac{3 + 4 B - 75}{2}

A = \frac{- ( - 3 ) - 4 B - 75}{2 \cdot 1} : \frac{3 - 4 B - 75}{2}

The solutions to the quadratic equation are:

A = \frac{3 + 4 B - 75}{2}, A = \frac{3 - 4 B - 75}{2}

(2 x + 3)^{2} + (x + 4)^{2} = 10

x^{2} + 2 x - 4 = 4

5 x^{2} + 19 x + 12 = 0

- x^{2} + 13 = 3 x

9 x^{2} - 6 x - 11 = 0

What are the solutions to the equation solvefor A,B=A^2-3A+21 ?
The solutions to the equation solvefor A,B=A^2-3A+21 are A=(3+sqrt(4B-75))/2 ,A=(3-sqrt(4B-75))/2
Find the zeros of solvefor A,B=A^2-3A+21
The zeros of solvefor A,B=A^2-3A+21 are A=(3+sqrt(4B-75))/2 ,A=(3-sqrt(4B-75))/2