4x+2=6x2+3x

Solution for 4x+2=6x2+3x equation:

4x+2=6x^2+3x

We move all terms to the left:

4x+2-(6x^2+3x)=0

We get rid of parentheses

-6x^2+4x-3x+2=0

We add all the numbers together, and all the variables

-6x^2+x+2=0

a = -6; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-6)·2
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*-6}=\frac{-8}{-12}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*-6}=\frac{6}{-12}
=-1/2
$