Question

Consider the quadratic equation below. 4x^2-5=3x+4 Determine the correct set-up for solving the equation using the quadratic formula.

Answer 1

$4x^2-5=3x+4$

$4x^2 - 3x - 5 - 4 = 0$

$4x^2 - 3x -9 = 0$

$x= \dfrac{3 \pm \sqrt{3^2 - 4(4)(-9)}}{2(4)}$

$x = \frac 1 8 (3 \pm \sqrt{9(1 + 16)})$

$x = \frac 1 8 (3 \pm 3\sqrt{17})$

Answer 2

Answer:

Solutions are 1.92 and -1.17

Step-by-step explanation:

The general solutions of quadratic equation of the form ax²+bx+c = 0 is given by $\frac{-b+\sqrt{b^2-4ac} }{2a}$ and $\frac{-b-\sqrt{b^2-4ac} }{2a}$

Here the the equation is 4x²-5 = 3x + 4

On rearranging

             4x²-3x-5-4 = 0

             4x²-3x-9 = 0

Comparing with ax²+bx+c = 0, we will get a = 4, b = -3 and c = -9

The solutions are given by

     $\frac{-(-3)+\sqrt{(-3)^2-4*4*(-9)} }{2*4}$ and  $\frac{-(-3)-\sqrt{(-3)^2-4*4*(-9)} }{2*4}$

     $\frac{3+\sqrt{153} }{8}$ and  $\frac{3-\sqrt{153} }{8}$

     1.92 and -1.17