6x+2=9x2+3x

Solution for 6x+2=9x2+3x equation:

6x+2=9x^2+3x

We move all terms to the left:

6x+2-(9x^2+3x)=0

We get rid of parentheses

-9x^2+6x-3x+2=0

We add all the numbers together, and all the variables

-9x^2+3x+2=0

a = -9; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-9)·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-9}=\frac{-12}{-18}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-9}=\frac{6}{-18}
=-1/3
$