How do you solve using the quadratic formula #6x+9=2x^2#?

2 Answers
Apr 13, 2018

Answer:

#x=3/2+3/2 sqrt 3# or #x=3/2-3/2 sqrt 3#

Explanation:

#6x+9=2x^2#

#:.2x^2=6x+9#

#:.2x^2-6x-9=0#

Quadratic formula:- #x=ax^2+bx+c#

#:.a=2,b=-6 and c=-9#

#:.x=(-b+-sqrt (b^2-4ac))/(2a)#

#:.x=(-(-6)+-sqrt((-6^2)-4(2)(-9)))/(2(2))#

#:.x=(6+-sqrt(108))/4#

#:.x=(6+-sqrt(3*3*3*2*2))/4#

#:.sqrt2*sqrt2=2#

#:.sqrt 3*sqrt 3=3#

#:.x=(6+-3*2 sqrt 3)/4#

#:.x=(6+-6 sqrt 3)/4#

#:.x=cancel 6^3/cancel 4^2+-(cancel 6^3 sqrt 3)/cancel 4^2#

#:.x=3/2+-(3 sqrt 3)/2#

#:.x=3/2+3/2 sqrt 3# or #x=3/2-3/2 sqrt 3#

Apr 13, 2018

Answer:

#x=3/2+−3/2sqrt(3) or x=3/2+3/2sqrt3#

Explanation:

Step 1: Subtract #2x^2# from both sides.
#6x+9−color(blue)(2x^2)=2x^2−color(blue)(2x^2)#
#−2x^2+6x+9=0#
Step 2: Use quadratic formula with #color(red)(a=-2), color(purple)(b=6), color(green)(c=9).#
#x=−b±sqrt(b^2−4ac)/(2a)#
#x=−(color(purple)(6))^2±sqrt((color(purple)(6))^2−4(color(red)(−2))(color(green)(9)))/(2(color(red)(−2))#
x=
#−6±sqrt108/(−4)#
#x=3/2+−3/2sqrt3# or #x=3/2+3/2 sqrt3#