What are the solutions to the equation (3/2 x+5)*(7/2 x-6)=30 ?

The solutions to the equation (3/2 x+5)*(7/2 x-6)=30 are x= 8/3 ,x=-30/7

Find the zeros of (3/2 x+5)*(7/2 x-6)=30

The zeros of (3/2 x+5)*(7/2 x-6)=30 are x= 8/3 ,x=-30/7

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(\frac{3}{2} x + 5) \cdot (\frac{7}{2} x - 6) = 30

x = \frac{8}{3}, x = - \frac{30}{7}

Decimal Notation

x = 2.66666 \dots, x = - 4.28571 \dots

Solution steps

(\frac{3}{2} x + 5) (\frac{7}{2} x - 6) = 30

Expand

(\frac{3}{2} x + 5) (\frac{7}{2} x - 6) : \frac{21}{4} x^{2} + \frac{17}{2} x - 30

\frac{21}{4} x^{2} + \frac{17}{2} x - 30 = 30

Move

30

to the left side

\frac{21}{4} x^{2} + \frac{17}{2} x - 60 = 0

Write in the standard form

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

\frac{21 x ^{2}}{4} + \frac{17 x}{2} - 60 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- \frac{17}{2} \pm ( \frac{17}{2} ) ^{2} - 4 \cdot \frac{21}{4} ( - 60 )}{2 \cdot \frac{21}{4}}

(\frac{17}{2})^{2} - 4 \cdot \frac{21}{4} (- 60) = \frac{73}{2}

x_{1, 2} = \frac{- \frac{17}{2} \pm \frac{73}{2}}{2 \cdot \frac{21}{4}}

Separate the solutions

x_{1} = \frac{- \frac{17}{2} + \frac{73}{2}}{2 \cdot \frac{21}{4}}, x_{2} = \frac{- \frac{17}{2} - \frac{73}{2}}{2 \cdot \frac{21}{4}}

x = \frac{- \frac{17}{2} + \frac{73}{2}}{2 \frac{21}{4}} : \frac{8}{3}

x = \frac{- \frac{17}{2} - \frac{73}{2}}{2 \frac{21}{4}} : - \frac{30}{7}

The solutions to the quadratic equation are:

x = \frac{8}{3}, x = - \frac{30}{7}

\frac{1}{4} (4 u + 12) - 1 = 12

∣ 6 - 3 x ∣ - 6 = 9

\frac{x - 1}{x + 2} > 0

x^{2} + 4 x \leq 0

2 x^{2} + 9 x = 0

What are the solutions to the equation (3/2 x+5)*(7/2 x-6)=30 ?
The solutions to the equation (3/2 x+5)*(7/2 x-6)=30 are x= 8/3 ,x=-30/7
Find the zeros of (3/2 x+5)*(7/2 x-6)=30
The zeros of (3/2 x+5)*(7/2 x-6)=30 are x= 8/3 ,x=-30/7