Solve for x 2x^2+7x=4

Problem

2*x2+7*x=4

Solution

1. Rearrange the equation into standard quadratic form a*x2+b*x+c=0 by subtracting 4 from both sides.

2*x2+7*x−4=0

2. Identify the coefficients for the quadratic formula where a=2 b=7 and c=−4

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values into the quadratic formula.

x=(−7±√(,7−4*(2)*(−4)))/(2*(2))

4. Simplify the expression inside the square root (the discriminant).

x=(−7±√(,49+32))/4

x=(−7±√(,81))/4

5. Evaluate the square root.

x=(−7±9)/4

6. Solve for both possible values of x

x=(−7+9)/4⇒x=2/4⇒x=1/2

x=(−7−9)/4⇒x=(−16)/4⇒x=−4

Final Answer

x=1/2,−4

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