What are the solutions to the equation x(2x+1)-5(x-2)=6 ?

The solutions to the equation x(2x+1)-5(x-2)=6 are x=1+i,x=1-i

Find the zeros of x(2x+1)-5(x-2)=6

The zeros of x(2x+1)-5(x-2)=6 are x=1+i,x=1-i

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x (2 x + 1) - 5 (x - 2) = 6

x = 1 + i, x = 1 - i

Solution steps

x (2 x + 1) - 5 (x - 2) = 6

Expand

x (2 x + 1) - 5 (x - 2) : 2 x^{2} - 4 x + 10

2 x^{2} - 4 x + 10 = 6

Move

6

to the left side

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

Solve with the quadratic formula

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

Simplify

(- 4)^{2} - 4 \cdot 2 \cdot 4 : 4 i

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

Separate the solutions

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

x = \frac{- ( - 4 ) + 4 i}{2 \cdot 2} : 1 + i

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

The solutions to the quadratic equation are:

x = 1 + i, x = 1 - i

(3 x + 1) (3 x - 1) + x = 4 x^{2} - 3

15 x^{2} = 90 x

5 x^{2} + 8 x - 23 = 0

x + 1 = x^{2} + 1

0 = (x + 1)^{2} - 4

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