x+4=3x2

Solution for x+4=3x2 equation:

x+4=3x^2

We move all terms to the left:

x+4-(3x^2)=0

determiningTheFunctionDomain
-3x^2+x+4=0

a = -3; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-3)·4
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-3}=\frac{6}{-6}
=-1
$