Answer:
\(x= \frac{7}{4},-1\) is the required solution.
Step-by-step explanation:
We have been given the equation:
\(\frac{3}{2}\cdot \frac{x+7}{2}=x^2\)
We will solve for x to get the solution of the equation
After first step of simplification we get:
\(\frac{3x}{2}+\frac{7}{2}=2x^2\)
Now, distribute the parenthesis on left hand side of the equation:
\(3x+7=4x^2\)
\(4x^2-3x-7=0\)
We will solve the above quadratic equation by discriminant rule
\(x=\frac{-b\pm\sqrt{D}}{2a}\)
Where, \(D=b^2-4ac\)
We will compare the equation with general quadratic equation:
\(ax^2+bx+c=0\)
Here, a=4,b= -3 and c=-7 on substituting the values we get:
\(D=(-3)^2-4(4)(-7)\)
\(D=9+112=121\)
Now for x
\(x=\frac{-(-3)\pm\sqrt{121}}{2\cdot 4}\)
\(x= \frac{3\pm\11}{8}\)
\(\Rightarrow \frac{14}{8},\frac{-8}{8}\)
\(\Rightarrow \frac{7}{4},-1\)
