Question

16x^2-24x+7=0 equation and/or inequalities

Answer 1

It is quadratic equation.
First we have find delta given by formula: delta=$b^{2}-4ac$
where our 
a=16
b=-24
c=7
so, delta=$24^{2}-4*16*7=128$
Because delta is positive, there is real results.
Now we can use next formula x=$\frac{-b+ \sqrt{delta} }{2a}$
, to find roots (results, 2 results because its quadratic equation and delta is greater than 0)
x1=$\frac{24+ \sqrt{128} }{2*16} = \frac{3+ \sqrt{2} }{4}$
x2=$\frac{24- \sqrt{128} }{2*16} = \frac{3- \sqrt{2} }{4}$ 

Answer 2

$16x^2-24x+7=0\\ 16x^2-24x+9-2=0\\ (4x-3)^2=2\\ 4x-3=\sqrt2 \vee 4x-3=-\sqrt2\\ 4x=3+\sqrt2 \vee 4x=3-\sqrt2\\ x=\frac{3+\sqrt2}{4} \vee x=\frac{3-\sqrt2}{4}$