What are the solutions to the equation 3/5 x(x-4)-1/2 (x-3)=2 ?

The solutions to the equation 3/5 x(x-4)-1/2 (x-3)=2 are x=5,x=-1/6

Find the zeros of 3/5 x(x-4)-1/2 (x-3)=2

The zeros of 3/5 x(x-4)-1/2 (x-3)=2 are x=5,x=-1/6

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\frac{3}{5} x (x - 4) - \frac{1}{2} (x - 3) = 2

x = 5, x = - \frac{1}{6}

Decimal Notation

x = 5, x = - 0.16666 \dots

Solution steps

\frac{3}{5} x (x - 4) - \frac{1}{2} (x - 3) = 2

Find Least Common Multiplier of

5, 2 : 10

Multiply by LCM=

10

\frac{3}{5} x (x - 4) \cdot 10 - \frac{1}{2} (x - 3) \cdot 10 = 2 \cdot 10

Simplify

6 x (x - 4) - 5 (x - 3) = 20

Expand

6 x (x - 4) - 5 (x - 3) : 6 x^{2} - 29 x + 15

6 x^{2} - 29 x + 15 = 20

Move

20

to the left side

6 x^{2} - 29 x - 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 29 ) \pm ( - 29 ) ^{2} - 4 \cdot 6 ( - 5 )}{2 \cdot 6}

(- 29)^{2} - 4 \cdot 6 (- 5) = 31

x_{1, 2} = \frac{- ( - 29 ) \pm 31}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 29 ) + 31}{2 \cdot 6}, x_{2} = \frac{- ( - 29 ) - 31}{2 \cdot 6}

x = \frac{- ( - 29 ) + 31}{2 \cdot 6} : 5

x = \frac{- ( - 29 ) - 31}{2 \cdot 6} : - \frac{1}{6}

The solutions to the quadratic equation are:

x = 5, x = - \frac{1}{6}

x^{2} - 11 x + 28 = 0

y^{2} - y + 3 = 0

8 x^{2} - 4 x - 24 = 0

- 6 x = x^{2} + 9

x, f = I n (3 x^{2} - 5 x + 2)

What are the solutions to the equation 3/5 x(x-4)-1/2 (x-3)=2 ?
The solutions to the equation 3/5 x(x-4)-1/2 (x-3)=2 are x=5,x=-1/6
Find the zeros of 3/5 x(x-4)-1/2 (x-3)=2
The zeros of 3/5 x(x-4)-1/2 (x-3)=2 are x=5,x=-1/6