Answer:
[tex]x=\frac{-\sqrt{5}+3}{2}[/tex] and [tex]x=\frac{\sqrt{5}+3}{2}[/tex]
Step-by-step explanation:
[tex]4x^2-12x+9=5[/tex]
To solve for x we need to make right hand side 0
Subtract 5 on both sides
[tex]4x^2-12x+4=0[/tex]
Divide whole equation by 4
[tex]x^2-3x+1=0[/tex]
Apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
the value of a=1, b=-3 and c=1
[tex]x=\frac{-(-3)+-\sqrt{(-3)^2-4(1)(1)}}{2(1)}[/tex]
[tex]x=\frac{3+-\sqrt{5}}{2}[/tex]
[tex]x=\frac{-\sqrt{5}+3}{2}[/tex] and [tex]x=\frac{\sqrt{5}+3}{2}[/tex]
