Question

3x^2 + 5x =8

Solve with the quadratic formula. I messed up somewhere in my solving... Steps would be great~!

Answer 1

quadratic formula

for ax^2+bx+c=0
x=
`(-b+/- √(b^2-4ac) )/(2a)`

first conver to ax^2+bx+c=0 form

3x^2+5x=8
minus 8 both sides
3x^2+5x-8=0
we can actually solve by factoring (x-1)(3x+8), but that's isn't the question

so

ax^2+bx+c=0
3x^2+5x-8=0
a=3
b=5
c=-8

x=
`(-5+/- √(5^2-4(3)(-8)) )/(2(3))`
x=
`(-5+/- √(25+96) )/(6)`
x=
`(-5+/- √(121) )/(6)`
x=
`(-5+/-11)/(6)`
so
x=(-5-11)/6 or (-5+11)/6
simplify
(-5-11)/6=-16/6=-8/3
(-5+11)/6=6/6=1

x=-8/3 and 1

Answer 2

Just plot the function and mark the points it crosses through.


X has two solutions = -8/3 & 1