Find point of intersection of 20/7 x^2-260/7 x=96/5 x-80
Starting with the given equation:
20/7 x^2 - 260/7 x = 96/5 x - 80
We want to solve for x to find the point(s) of intersection. First, we'll move all the x terms to one side and all the constants to the other side:
20/7 x^2 - 260/7 x - 96/5 x + 80 = 0
Now, we'll combine like terms:
20/7 x^2 - 692/35 x + 80 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 20/7, b = -692/35, and c = 80:
x = (-(-692/35) ± sqrt((-692/35)^2 - 4(20/7)(80))) / (2(20/7))
Simplifying:
x = (692/35 ± sqrt(1984/1225)) / (40/7)
x = (692/35 ± 8/35 √31) / (40/7)
Now, we can simplify further:
x = (7/5)(692/35 ± 8/35 √31)
x = (14/5)(346/35 ± 4/35 √31)
x = (14/5)(10 ± √31)
So the two points of intersection are:
(14/5)(10 + √31) and (14/5)(10 - √31)