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

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

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

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

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

x = 3, x = \frac{6}{5}

Decimal Notation

x = 3, x = 1.2

Solution steps

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

Multiply both sides by

2

5 x (x - 3) = 6 (x - 5) + 12

Expand

5 x (x - 3) : 5 x^{2} - 15 x

Expand

6 (x - 5) + 12 : 6 x - 18

5 x^{2} - 15 x = 6 x - 18

Move

18

to the left side

5 x^{2} - 15 x + 18 = 6 x

Move

6 x

to the left side

5 x^{2} - 21 x + 18 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 21 ) \pm ( - 21 ) ^{2} - 4 \cdot 5 \cdot 18}{2 \cdot 5}

(- 21)^{2} - 4 \cdot 5 \cdot 18 = 9

x_{1, 2} = \frac{- ( - 21 ) \pm 9}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 21 ) + 9}{2 \cdot 5}, x_{2} = \frac{- ( - 21 ) - 9}{2 \cdot 5}

x = \frac{- ( - 21 ) + 9}{2 \cdot 5} : 3

x = \frac{- ( - 21 ) - 9}{2 \cdot 5} : \frac{6}{5}

The solutions to the quadratic equation are:

x = 3, x = \frac{6}{5}

2 j^{2} + 11 j + 12

5 x z - 5 yz - x + y

x^{2} + 8 x = - 12

(x - 5) (x + 1) = 0

3 x^{2} + 22 x + 7

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