# How do you solve x + 4 = 3x²?

Mar 24, 2016

$x = \frac{4}{3} , - 1$

#### Explanation:

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

$\rightarrow x = 3 {x}^{2} - 4$

$\rightarrow 0 = 3 {x}^{2} - 4 - x$

Rewrite in standard form

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

This is a Quadratic equation (in form $a {x}^{2} + b x + c = 0$)

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

Where

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

$\rightarrow x = \frac{- \left(- 1\right) \pm \sqrt{- {1}^{2} - 4 \left(3\right) \left(- 4\right)}}{2 \left(3\right)}$

$\rightarrow x = \frac{1 \pm \sqrt{1 - 4 \left(- 12\right)}}{6}$

$\rightarrow x = \frac{1 \pm \sqrt{1 - \left(- 48\right)}}{6}$

$\rightarrow x = \frac{1 \pm \sqrt{49}}{6}$

$\rightarrow x = \frac{1 \pm 7}{6}$

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|