Question

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

Answer 1

`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=(3+\sqrt2)/(4) \vee x=(3-\sqrt2)/(4)`

Answer 2

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=
`(-b+ √(delta) )/(2a)`
, to find roots (results, 2 results because its quadratic equation and delta is greater than 0)
x1=
`(24+ √(128) )/(2*16) = (3+ √(2) )/(4)`
x2=
`(24- √(128) )/(2*16) = (3- √(2) )/(4)`