What are the solutions to the equation 13x-1.65x^2=23.8 ?

The solutions to the equation 13x-1.65x^2=23.8 are x=(2(65-sqrt(298)))/(33),x=(2(65+sqrt(298)))/(33)

Find the zeros of 13x-1.65x^2=23.8

The zeros of 13x-1.65x^2=23.8 are x=(2(65-sqrt(298)))/(33),x=(2(65+sqrt(298)))/(33)

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13 x - 1.65 x^{2} = 23.8

x = \frac{2 ( 65 - 298 )}{33}, x = \frac{2 ( 65 + 298 )}{33}

Decimal Notation

x = 2.89317 \dots, x = 4.98561 \dots

Solution steps

13 x - 1.65 x^{2} = 23.8

Multiply both sides by

100

1300 x - 165 x^{2} = 2380

Move

2380

to the left side

1300 x - 165 x^{2} - 2380 = 0

Write in the standard form

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

- 165 x^{2} + 1300 x - 2380 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1300 \pm 130 0 ^{2} - 4 ( - 165 ) ( - 2380 )}{2 ( - 165 )}

130 0^{2} - 4 (- 165) (- 2380) = 20298

x_{1, 2} = \frac{- 1300 \pm 20 298}{2 ( - 165 )}

Separate the solutions

x_{1} = \frac{- 1300 + 20 298}{2 ( - 165 )}, x_{2} = \frac{- 1300 - 20 298}{2 ( - 165 )}

x = \frac{- 1300 + 20 298}{2 ( - 165 )} : \frac{2 ( 65 - 298 )}{33}

x = \frac{- 1300 - 20 298}{2 ( - 165 )} : \frac{2 ( 65 + 298 )}{33}

The solutions to the quadratic equation are:

x = \frac{2 ( 65 - 298 )}{33}, x = \frac{2 ( 65 + 298 )}{33}

\frac{5}{4} x^{2} + 7 x + 9 = 0

y, y x^{2} - 4 y - x^{2} = 0

n (x) = - x^{2} + 8 x - 9

(x + 8) (4 x + 1) = 0

y, x = a - 2 b y^{2}

What are the solutions to the equation 13x-1.65x^2=23.8 ?
The solutions to the equation 13x-1.65x^2=23.8 are x=(2(65-sqrt(298)))/(33),x=(2(65+sqrt(298)))/(33)
Find the zeros of 13x-1.65x^2=23.8
The zeros of 13x-1.65x^2=23.8 are x=(2(65-sqrt(298)))/(33),x=(2(65+sqrt(298)))/(33)