What are the solutions to the equation (-4/3 b+9/2)^2+b^2-(-4/3 b+9/2)-6b=-3 ?

The solutions to the equation (-4/3 b+9/2)^2+b^2-(-4/3 b+9/2)-6b=-3 are b= 9/2 ,b= 3/2

Find the zeros of (-4/3 b+9/2)^2+b^2-(-4/3 b+9/2)-6b=-3

The zeros of (-4/3 b+9/2)^2+b^2-(-4/3 b+9/2)-6b=-3 are b= 9/2 ,b= 3/2

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(- \frac{4}{3} b + \frac{9}{2})^{2} + b^{2} - (- \frac{4}{3} b + \frac{9}{2}) - 6 b = - 3

b = \frac{9}{2}, b = \frac{3}{2}

Decimal Notation

b = 4.5, b = 1.5

Solution steps

(- \frac{4}{3} b + \frac{9}{2})^{2} + b^{2} - (- \frac{4}{3} b + \frac{9}{2}) - 6 b = - 3

Expand

(- \frac{4}{3} b + \frac{9}{2})^{2} + b^{2} - (- \frac{4}{3} b + \frac{9}{2}) - 6 b : \frac{63}{4} + \frac{25}{9} b^{2} - \frac{50}{3} b

\frac{63}{4} + \frac{25}{9} b^{2} - \frac{50}{3} b = - 3

Move

3

to the left side

\frac{75}{4} + \frac{25}{9} b^{2} - \frac{50}{3} b = 0

Write in the standard form

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

\frac{25 b ^{2}}{9} - \frac{50 b}{3} + \frac{75}{4} = 0

Solve with the quadratic formula

b_{1, 2} = \frac{- ( - \frac{50}{3} ) \pm ( - \frac{50}{3} ) ^{2} - 4 \cdot \frac{25}{9} \cdot \frac{75}{4}}{2 \cdot \frac{25}{9}}

(- \frac{50}{3})^{2} - 4 \cdot \frac{25}{9} \cdot \frac{75}{4} = \frac{25}{3}

b_{1, 2} = \frac{- ( - \frac{50}{3} ) \pm \frac{25}{3}}{2 \cdot \frac{25}{9}}

Separate the solutions

b_{1} = \frac{- ( - \frac{50}{3} ) + \frac{25}{3}}{2 \cdot \frac{25}{9}}, b_{2} = \frac{- ( - \frac{50}{3} ) - \frac{25}{3}}{2 \cdot \frac{25}{9}}

b = \frac{- ( - \frac{50}{3} ) + \frac{25}{3}}{2 \frac{25}{9}} : \frac{9}{2}

b = \frac{- ( - \frac{50}{3} ) - \frac{25}{3}}{2 \frac{25}{9}} : \frac{3}{2}

The solutions to the quadratic equation are:

b = \frac{9}{2}, b = \frac{3}{2}

2 y^{2} + 11 y + 12 = 0

x^{2} + 49 = - 14 x

4 (2 x - 1)^{2} = 8

(x) = - 10 x^{2} - 2500 x + 1000000

4 v^{2} - 15 v + 5 = - 3 v

What are the solutions to the equation (-4/3 b+9/2)^2+b^2-(-4/3 b+9/2)-6b=-3 ?
The solutions to the equation (-4/3 b+9/2)^2+b^2-(-4/3 b+9/2)-6b=-3 are b= 9/2 ,b= 3/2
Find the zeros of (-4/3 b+9/2)^2+b^2-(-4/3 b+9/2)-6b=-3
The zeros of (-4/3 b+9/2)^2+b^2-(-4/3 b+9/2)-6b=-3 are b= 9/2 ,b= 3/2