For this case we have the following quadratic equation:
[tex] 2x ^ 2 = 4x - 7[/tex]
Rewriting the equation we have:
[tex]2x ^ 2 - 4x + 7 = 0[/tex]
From here, we have:
[tex]a=2 b = -4c = 7[/tex]
Substituting values in the quadratic equation we have:
[tex] x = \frac{-b+/-\sqrt{b^2-4ac}}{2a} [/tex]
[tex] x = \frac{-(-4)+/-\sqrt{(-4)^2-4(2)(7)}}{2(2)} [/tex]
Rewriting the equation we have:
[tex] x = \frac{4+/-\sqrt{16-56}}{4} [/tex]
[tex] x = \frac{4+/-\sqrt{-40}}{4} [/tex]
[tex] x = \frac{4+/-\sqrt{-4*10}}{4} [/tex]
[tex] x = \frac{4+/-2i\sqrt{*10}}{4} [/tex]
[tex] x = \frac{2+/-i\sqrt{*10}}{2} [/tex]
Answer:
The values of x are given by:
[tex] x = \frac{2+i\sqrt{*10}}{2} [/tex]
[tex] x = \frac{2-i\sqrt{*10}}{2} [/tex]
