[tex] \frac{-1}{2x+3} =-x+7[/tex]
times both sides by (2x+3)
-1=(2x+3)(-x+7)
distribute or foil or expand
-1=-2x²+11x+21
times -1 both sides
1=2x²-11x-21
minus 1 from both sides
0=2x²-11x-22
factor
use quadratic formula
for
0=ax²+bx+c
x=[tex] \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
given
0=2x²-11x-22
a=2
b=-11
c=-22
x=[tex] \frac{-(-11)+/- \sqrt{(-11)^2-4(2)(-22)} }{2(2)} [/tex]
x=[tex] \frac{11+/- \sqrt{121+176} }{4} [/tex]
x=[tex] \frac{11+/- \sqrt{297} }{4} [/tex]
x=[tex] \frac{11+/- 3\sqrt{33} }{4} [/tex]
x=[tex] \frac{11+ 3\sqrt{33} }{4} [/tex] or [tex] \frac{11- 3\sqrt{33} }{4} [/tex]
