# Solve for y 72y^2+1=12y 72y2+1=12y
Subtract 12y from both sides of the equation.
72y2+1-12y=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=72, b=-12, and c=1 into the quadratic formula and solve for y.
12±(-12)2-4⋅(72⋅1)2⋅72
Simplify.
Simplify the numerator.
Raise -12 to the power of 2.
y=12±144-4⋅(72⋅1)2⋅72
Multiply 72 by 1.
y=12±144-4⋅722⋅72
Multiply -4 by 72.
y=12±144-2882⋅72
Subtract 288 from 144.
y=12±-1442⋅72
Rewrite -144 as -1(144).
y=12±-1⋅1442⋅72
Rewrite -1(144) as -1⋅144.
y=12±-1⋅1442⋅72
Rewrite -1 as i.
y=12±i⋅1442⋅72
Rewrite 144 as 122.
y=12±i⋅1222⋅72
Pull terms out from under the radical, assuming positive real numbers.
y=12±i⋅122⋅72
Move 12 to the left of i.
y=12±12i2⋅72
y=12±12i2⋅72
Multiply 2 by 72.
y=12±12i144
Simplify 12±12i144.
y=1±i12
y=1±i12
The final answer is the combination of both solutions.
y=112+i12,112-i12
Solve for y 72y^2+1=12y

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