ANSWER
[tex]x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2} [/tex]
EXPLANATION
The given quadratic equation is:
[tex] 2{x}^{2} - 10x + 7 = 0[/tex]
Comparing this equation to
[tex] a{x}^{2} + bx + c = 0[/tex]
we have
a=2, b=-10 and c=7.
The solution is given by the quadratic formula;
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
We plug in the values to get,
[tex]x = \frac{ - - 10 \pm \sqrt{ {( - 10)}^{2} - 4(2)(7) } }{2(2)} [/tex]
This implies that
[tex]x = \frac{ 10 \pm \sqrt{ {100} - 56 } }{4} [/tex]
[tex]x = \frac{ 10 \pm \sqrt {44 } }{4} [/tex]
[tex]x = \frac{ 10 \pm 2\sqrt {11 } }{4} [/tex]
[tex]x = \frac{ 5 \pm \sqrt {11 } }{2}[/tex]
[tex]x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2} [/tex]
