What are the solutions to the equation x^2-15/2 x+45/4 =0 ?

The solutions to the equation x^2-15/2 x+45/4 =0 are x=(3(5+sqrt(5)))/4 ,x=(3(5-sqrt(5)))/4

Find the zeros of x^2-15/2 x+45/4 =0

The zeros of x^2-15/2 x+45/4 =0 are x=(3(5+sqrt(5)))/4 ,x=(3(5-sqrt(5)))/4

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x^{2} - \frac{15}{2} x + \frac{45}{4} = 0

x = \frac{3 ( 5 + 5 )}{4}, x = \frac{3 ( 5 - 5 )}{4}

Decimal Notation

x = 5.42705 \dots, x = 2.07294 \dots

Solution steps

x^{2} - \frac{15}{2} x + \frac{45}{4} = 0

Find Least Common Multiplier of

2, 4 : 4

Multiply by LCM=

4

x^{2} \cdot 4 - \frac{15}{2} x \cdot 4 + \frac{45}{4} \cdot 4 = 0 \cdot 4

Simplify

4 x^{2} - 30 x + 45 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 30 ) \pm ( - 30 ) ^{2} - 4 \cdot 4 \cdot 45}{2 \cdot 4}

(- 30)^{2} - 4 \cdot 4 \cdot 45 = 65

x_{1, 2} = \frac{- ( - 30 ) \pm 6 5}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 30 ) + 6 5}{2 \cdot 4}, x_{2} = \frac{- ( - 30 ) - 6 5}{2 \cdot 4}

x = \frac{- ( - 30 ) + 6 5}{2 \cdot 4} : \frac{3 ( 5 + 5 )}{4}

x = \frac{- ( - 30 ) - 6 5}{2 \cdot 4} : \frac{3 ( 5 - 5 )}{4}

The solutions to the quadratic equation are:

x = \frac{3 ( 5 + 5 )}{4}, x = \frac{3 ( 5 - 5 )}{4}

6 x^{2} - 18 x - 108 = 0

x^{2} + 20 x + 19 = 0

- 25 x^{2} - 15 x = 0

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

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

What are the solutions to the equation x^2-15/2 x+45/4 =0 ?
The solutions to the equation x^2-15/2 x+45/4 =0 are x=(3(5+sqrt(5)))/4 ,x=(3(5-sqrt(5)))/4
Find the zeros of x^2-15/2 x+45/4 =0
The zeros of x^2-15/2 x+45/4 =0 are x=(3(5+sqrt(5)))/4 ,x=(3(5-sqrt(5)))/4