How do you solve x + 4 = 3x²?

1 Answer
Mar 24, 2016

x=4/3,-1

Explanation:

color(blue)(x+4=3x^2

rarrx=3x^2-4

rarr0=3x^2-4-x

Rewrite in standard form

color(purple)(rarr3x^2-x-4=0

This is a Quadratic equation (in form ax^2+bx+c=0)

Use Quadratic formula

color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)

Where

color(red)(a=3,b=-1,c=-4

rarrx=(-(-1)+-sqrt(-1^2-4(3)(-4)))/(2(3))

rarrx=(1+-sqrt(1-4(-12)))/(6)

rarrx=(1+-sqrt(1-(-48)))/(6)

rarrx=(1+-sqrt(49))/(6)

rarrx=(1+-7)/(6)

Now we have 2 values for x

color(indigo)( x=(1+7)/(6)=8/6=4/3

color(orange)(x=(1-7)/(6)=-6/6=-1

color(blue)(ul bar |x=4/3,-1|