# Solve for z (z^2)/3-z=5/3 z23-z=53
Move 53 to the left side of the equation by subtracting it from both sides.
z23-z-53=0
Multiply through by the least common denominator 3, then simplify.
Apply the distributive property.
3(z23)+3(-z)+3(-53)=0
Simplify.
Cancel the common factor of 3.
Cancel the common factor.
3(z23)+3(-z)+3(-53)=0
Rewrite the expression.
z2+3(-z)+3(-53)=0
z2+3(-z)+3(-53)=0
Multiply -1 by 3.
z2-3z+3(-53)=0
Cancel the common factor of 3.
Move the leading negative in -53 into the numerator.
z2-3z+3(-53)=0
Cancel the common factor.
z2-3z+3(-53)=0
Rewrite the expression.
z2-3z-5=0
z2-3z-5=0
z2-3z-5=0
z2-3z-5=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-3, and c=-5 into the quadratic formula and solve for z.
3±(-3)2-4⋅(1⋅-5)2⋅1
Simplify.
Simplify the numerator.
Raise -3 to the power of 2.
z=3±9-4⋅(1⋅-5)2⋅1
Multiply -5 by 1.
z=3±9-4⋅-52⋅1
Multiply -4 by -5.
z=3±9+202⋅1
Add 9 and 20.
z=3±292⋅1
z=3±292⋅1
Multiply 2 by 1.
z=3±292
z=3±292
The final answer is the combination of both solutions.
z=3+292,3-292
The result can be shown in multiple forms.
Exact Form:
z=3+292,3-292
Decimal Form:
z=4.19258240…,-1.19258240…
Solve for z (z^2)/3-z=5/3

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