What are the solutions to the equation (2x^2-8)/5-(3x-9)/(10)=x-1 ?

The solutions to the equation (2x^2-8)/5-(3x-9)/(10)=x-1 are x=3,x= 1/4

Find the zeros of (2x^2-8)/5-(3x-9)/(10)=x-1

The zeros of (2x^2-8)/5-(3x-9)/(10)=x-1 are x=3,x= 1/4

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\frac{2 x ^{2} - 8}{5} - \frac{3 x - 9}{10} = x - 1

x = 3, x = \frac{1}{4}

Decimal Notation

x = 3, x = 0.25

Solution steps

\frac{2 x ^{2} - 8}{5} - \frac{3 x - 9}{10} = x - 1

Find Least Common Multiplier of

5, 10 : 10

Multiply by LCM=

10

\frac{2 x ^{2} - 8}{5} \cdot 10 - \frac{3 x - 9}{10} \cdot 10 = x \cdot 10 - 1 \cdot 10

Simplify

2 (2 x^{2} - 8) - (3 x - 9) = 10 x - 10

Expand

2 (2 x^{2} - 8) - (3 x - 9) : 4 x^{2} - 3 x - 7

4 x^{2} - 3 x - 7 = 10 x - 10

Move

10

to the left side

4 x^{2} - 3 x + 3 = 10 x

Move

10 x

to the left side

4 x^{2} - 13 x + 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 13 ) \pm ( - 13 ) ^{2} - 4 \cdot 4 \cdot 3}{2 \cdot 4}

(- 13)^{2} - 4 \cdot 4 \cdot 3 = 11

x_{1, 2} = \frac{- ( - 13 ) \pm 11}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 13 ) + 11}{2 \cdot 4}, x_{2} = \frac{- ( - 13 ) - 11}{2 \cdot 4}

x = \frac{- ( - 13 ) + 11}{2 \cdot 4} : 3

x = \frac{- ( - 13 ) - 11}{2 \cdot 4} : \frac{1}{4}

The solutions to the quadratic equation are:

x = 3, x = \frac{1}{4}

- x^{2} + 1 = 1

16 = (x + 7)^{2}

y, y^{2} = x^{3} (x - 2)

3 x^{2} - 24 x - 60 = 0

x^{2} - 18 x - 16 = - 9 x - 6

What are the solutions to the equation (2x^2-8)/5-(3x-9)/(10)=x-1 ?
The solutions to the equation (2x^2-8)/5-(3x-9)/(10)=x-1 are x=3,x= 1/4
Find the zeros of (2x^2-8)/5-(3x-9)/(10)=x-1
The zeros of (2x^2-8)/5-(3x-9)/(10)=x-1 are x=3,x= 1/4