ANSWER
[tex]x =1 +\frac{1}{2} \sqrt{ 10} \: or \: x =1 - \frac{1}{2}\: \sqrt{10}[/tex]
EXPLANATION
The given quadratic equation is
[tex]2 {x}^{2} - 4x - 3 = 0[/tex]
This function is of the form:
[tex] a{x}^{2} + bx + c = 0[/tex]
This implies that:
a=2, b=-4 and c=-3.
We can solve this equation using the quadratic formula:
[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
We substitute the values into the quadratic formula to obtain;
[tex]x = \frac{ - - 4 \pm \: \sqrt{ {( - 4)}^{2} - 4(2)( - 3)} }{2(2)} [/tex]
[tex]x = \frac{4 \pm \: \sqrt{ 40} }{4} [/tex]
[tex]x = \frac{4 \pm \: 2\sqrt{ 10} }{4}[/tex]
[tex]x =1\pm \: \frac{1}{2} \sqrt{10}[/tex]
[tex]x =1 +\frac{1}{2} \sqrt{ 10} \: or \: x =1 - \: \frac{1}{2} \sqrt{10}[/tex]
