6x^2 - 17x+13 = 20x^2 - 32
14x^2 + 17x - 45 = 0
(2x + 5)(7x - 9) = 0
2x + 5 = 0
2x = -5
x = -5/2
7x - 9 = 0
7x = 9
x = 9/7
Answer
x = -5/2 , 9/7
Answer:
[tex]x=\frac{-5}{2}[/tex]
[tex]x=\frac{9}{7}[/tex]
Step-by-step explanation:
[tex]6x^2-17x+13=20x^2-32[/tex]
combine like terms and simplify the equation
Subtract 6x^2 from both sides
[tex]6x^2-17x+13=20x^2-32[/tex]
[tex]-17x+13=14x^2-32[/tex]
Add 17x on both sides
[tex]13=14x^2+17x-32[/tex]
Now subtract 13 from both sides
[tex]0=14x^2+17x-45[/tex]
Now we solve for x
Apply quadratic formula : a= 14, b= +17 and c= -45
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-17+-\sqrt{17^2-4(14)(-45)} }{2(14)}[/tex]
[tex]x=\frac{-17+-53}{28}[/tex]
Now make two equations
[tex]x=\frac{-17+53}{28}=\frac{-5}{2}[/tex]
[tex]x=\frac{-17-53}{28}=\frac{9}{7}[/tex]
