w-72=2w2-6w+56

Since w is on the right side of the equation, switch the sides so it is on the left side of the equation.

2w2-6w+56=w-72

Raise 7 to the power of 2.

2w2-6w+56=w-1⋅49

Multiply -1 by 49.

2w2-6w+56=w-49

2w2-6w+56=w-49

Subtract w from both sides of the equation.

2w2-6w+56-w=-49

Subtract w from -6w.

2w2-7w+56=-49

2w2-7w+56=-49

Move 49 to the left side of the equation by adding it to both sides.

2w2-7w+56+49=0

Add 56 and 49.

2w2-7w+105=0

2w2-7w+105=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=2, b=-7, and c=105 into the quadratic formula and solve for w.

7±(-7)2-4⋅(2⋅105)2⋅2

Simplify the numerator.

Raise -7 to the power of 2.

w=7±49-4⋅(2⋅105)2⋅2

Multiply 2 by 105.

w=7±49-4⋅2102⋅2

Multiply -4 by 210.

w=7±49-8402⋅2

Subtract 840 from 49.

w=7±-7912⋅2

Rewrite -791 as -1(791).

w=7±-1⋅7912⋅2

Rewrite -1(791) as -1⋅791.

w=7±-1⋅7912⋅2

Rewrite -1 as i.

w=7±i7912⋅2

w=7±i7912⋅2

Multiply 2 by 2.

w=7±i7914

w=7±i7914

The final answer is the combination of both solutions.

w=7+i7914,7-i7914

Solve for w w-7^2=2w^2-6w+56