What are the solutions to the equation 90x-135-2x^2+3x=45x ?

The solutions to the equation 90x-135-2x^2+3x=45x are x=(3(8-sqrt(34)))/2 ,x=(3(8+sqrt(34)))/2

Find the zeros of 90x-135-2x^2+3x=45x

The zeros of 90x-135-2x^2+3x=45x are x=(3(8-sqrt(34)))/2 ,x=(3(8+sqrt(34)))/2

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90 x - 135 - 2 x^{2} + 3 x = 45 x

x = \frac{3 ( 8 - 34 )}{2}, x = \frac{3 ( 8 + 34 )}{2}

Decimal Notation

x = 3.25357 \dots, x = 20.74642 \dots

Solution steps

90 x - 135 - 2 x^{2} + 3 x = 45 x

Refine

- 2 x^{2} + 93 x - 135 = 45 x

Move

45 x

to the left side

- 2 x^{2} + 48 x - 135 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 48 \pm 4 8 ^{2} - 4 ( - 2 ) ( - 135 )}{2 ( - 2 )}

4 8^{2} - 4 (- 2) (- 135) = 634

x_{1, 2} = \frac{- 48 \pm 6 34}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 48 + 6 34}{2 ( - 2 )}, x_{2} = \frac{- 48 - 6 34}{2 ( - 2 )}

x = \frac{- 48 + 6 34}{2 ( - 2 )} : \frac{3 ( 8 - 34 )}{2}

x = \frac{- 48 - 6 34}{2 ( - 2 )} : \frac{3 ( 8 + 34 )}{2}

The solutions to the quadratic equation are:

x = \frac{3 ( 8 - 34 )}{2}, x = \frac{3 ( 8 + 34 )}{2}

n^{2} - n - 1 = 0

7 m^{2} + 2 m - 4 = 0

h, (7 - h)^{2} + (2 - k)^{2} = 0

x (x - 35) = 0

13 x^{2} - 39 = - 26 x

What are the solutions to the equation 90x-135-2x^2+3x=45x ?
The solutions to the equation 90x-135-2x^2+3x=45x are x=(3(8-sqrt(34)))/2 ,x=(3(8+sqrt(34)))/2
Find the zeros of 90x-135-2x^2+3x=45x
The zeros of 90x-135-2x^2+3x=45x are x=(3(8-sqrt(34)))/2 ,x=(3(8+sqrt(34)))/2