(4x^2-25)/(2x-5)=14
we hates fractions so m ultiply both sides by (2x-5)
4x^2-25=14(2x-5)
4x^2-25=28x-70
add 70 to both sides
4x^2+45=28x
subtract 28x fromoth sides
4x^2-28x+45=0
use quadratic formula which is
if you have
ax^2+bx+c=0 then
x=[tex] \frac{-b+/- \sqrt{b^{2}-4ac} }{2a}
[/tex]
a=4
b=-28
c=45
subsitute
x=[tex] \frac{-(-28)+/- \sqrt{(-28)^{2}-4(4)(45)} }{2(4)}
[/tex]
x=[tex] \frac{28+/- \sqrt{784-720} }{8}
[/tex]
x=[tex] \frac{28+/- 8}{8}
[/tex]
x=[tex] \frac{5}{2}
[/tex] or [tex] \frac{9}{2}
[/tex]
if we were to put 5/2 for x, the deonomentor would be equal to zero, so it cannot be used
answer is
x=9/2
