What are the solutions to the equation (3x-9)^2=5x+7 ?

The solutions to the equation (3x-9)^2=5x+7 are x=(59+sqrt(817))/(18),x=(59-sqrt(817))/(18)

Find the zeros of (3x-9)^2=5x+7

The zeros of (3x-9)^2=5x+7 are x=(59+sqrt(817))/(18),x=(59-sqrt(817))/(18)

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(3 x - 9)^{2} = 5 x + 7

x = \frac{59 + 817}{18}, x = \frac{59 - 817}{18}

Decimal Notation

x = 4.86573 \dots, x = 1.68982 \dots

Solution steps

(3 x - 9)^{2} = 5 x + 7

Expand

(3 x - 9)^{2} : 9 x^{2} - 54 x + 81

9 x^{2} - 54 x + 81 = 5 x + 7

Move

7

to the left side

9 x^{2} - 54 x + 74 = 5 x

Move

5 x

to the left side

9 x^{2} - 59 x + 74 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 59 ) \pm ( - 59 ) ^{2} - 4 \cdot 9 \cdot 74}{2 \cdot 9}

(- 59)^{2} - 4 \cdot 9 \cdot 74 = 817

x_{1, 2} = \frac{- ( - 59 ) \pm 817}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- ( - 59 ) + 817}{2 \cdot 9}, x_{2} = \frac{- ( - 59 ) - 817}{2 \cdot 9}

x = \frac{- ( - 59 ) + 817}{2 \cdot 9} : \frac{59 + 817}{18}

x = \frac{- ( - 59 ) - 817}{2 \cdot 9} : \frac{59 - 817}{18}

The solutions to the quadratic equation are:

x = \frac{59 + 817}{18}, x = \frac{59 - 817}{18}

c^{2} - 5 c + 9 = 0

y (y - 13) + 6 y = 18

7 (x + 5) (x - 3) - 5 (x + 3) (x - 3) = 0

2 x^{2} + 20 x + 15 = 127

6 x^{2} - 46 x + 312 = 14 x

What are the solutions to the equation (3x-9)^2=5x+7 ?
The solutions to the equation (3x-9)^2=5x+7 are x=(59+sqrt(817))/(18),x=(59-sqrt(817))/(18)
Find the zeros of (3x-9)^2=5x+7
The zeros of (3x-9)^2=5x+7 are x=(59+sqrt(817))/(18),x=(59-sqrt(817))/(18)