What are the solutions to the equation 2x^2-1=13x ?

The solutions to the equation 2x^2-1=13x are x=(13+sqrt(177))/4 ,x=(13-sqrt(177))/4

Find the zeros of 2x^2-1=13x

The zeros of 2x^2-1=13x are x=(13+sqrt(177))/4 ,x=(13-sqrt(177))/4

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2 x^{2} - 1 = 13 x

x = \frac{13 + 177}{4}, x = \frac{13 - 177}{4}

Decimal Notation

x = 6.57603 \dots, x = - 0.07603 \dots

Solution steps

2 x^{2} - 1 = 13 x

Move

13 x

to the left side

2 x^{2} - 1 - 13 x = 0

Write in the standard form

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

2 x^{2} - 13 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 13 ) \pm ( - 13 ) ^{2} - 4 \cdot 2 ( - 1 )}{2 \cdot 2}

(- 13)^{2} - 4 \cdot 2 (- 1) = 177

x_{1, 2} = \frac{- ( - 13 ) \pm 177}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 13 ) + 177}{2 \cdot 2}, x_{2} = \frac{- ( - 13 ) - 177}{2 \cdot 2}

x = \frac{- ( - 13 ) + 177}{2 \cdot 2} : \frac{13 + 177}{4}

x = \frac{- ( - 13 ) - 177}{2 \cdot 2} : \frac{13 - 177}{4}

The solutions to the quadratic equation are:

x = \frac{13 + 177}{4}, x = \frac{13 - 177}{4}

\frac{( X - 3 )}{2} - \frac{( 3 X + 5 )}{3} = \frac{( 6 X )}{5}

- 3 (v + 2) = 2 (v + 6) + 7

(x - 8)^{2} + (x - 1)^{2} = x

2 x^{3} - 9 x^{2} + 4 x + 15 \geq 0

y^{2} + 14 y = - 3

What are the solutions to the equation 2x^2-1=13x ?
The solutions to the equation 2x^2-1=13x are x=(13+sqrt(177))/4 ,x=(13-sqrt(177))/4
Find the zeros of 2x^2-1=13x
The zeros of 2x^2-1=13x are x=(13+sqrt(177))/4 ,x=(13-sqrt(177))/4