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

The solutions to the equation x^2+3x(x-2)=5 are x=(3+sqrt(29))/4 ,x=(3-sqrt(29))/4

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

The zeros of x^2+3x(x-2)=5 are x=(3+sqrt(29))/4 ,x=(3-sqrt(29))/4

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

x = \frac{3 + 29}{4}, x = \frac{3 - 29}{4}

Decimal Notation

x = 2.09629 \dots, x = - 0.59629 \dots

Solution steps

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

Expand

x^{2} + 3 x (x - 2) : 4 x^{2} - 6 x

4 x^{2} - 6 x = 5

Move

5

to the left side

4 x^{2} - 6 x - 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 4 ( - 5 )}{2 \cdot 4}

(- 6)^{2} - 4 \cdot 4 (- 5) = 229

x_{1, 2} = \frac{- ( - 6 ) \pm 2 29}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 29}{2 \cdot 4}, x_{2} = \frac{- ( - 6 ) - 2 29}{2 \cdot 4}

x = \frac{- ( - 6 ) + 2 29}{2 \cdot 4} : \frac{3 + 29}{4}

x = \frac{- ( - 6 ) - 2 29}{2 \cdot 4} : \frac{3 - 29}{4}

The solutions to the quadratic equation are:

x = \frac{3 + 29}{4}, x = \frac{3 - 29}{4}

3 x - 2 x^{2} = 7

t, y = \frac{1}{2} a t^{2}

(x + 2)^{2} = 11

x^{2} + 40 = 144

2 x^{2} + 8 x - 15 = 0

What are the solutions to the equation x^2+3x(x-2)=5 ?
The solutions to the equation x^2+3x(x-2)=5 are x=(3+sqrt(29))/4 ,x=(3-sqrt(29))/4
Find the zeros of x^2+3x(x-2)=5
The zeros of x^2+3x(x-2)=5 are x=(3+sqrt(29))/4 ,x=(3-sqrt(29))/4