18x-2=9x^2+6x+1

Solution for 18x-2=9x^2+6x+1 equation:

18x-2=9x^2+6x+1

We move all terms to the left:

18x-2-(9x^2+6x+1)=0

We get rid of parentheses

-9x^2+18x-6x-1-2=0

We add all the numbers together, and all the variables

-9x^2+12x-3=0

a = -9; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·(-9)·(-3)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6}{2*-9}=\frac{-18}{-18}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6}{2*-9}=\frac{-6}{-18}
=1/3
$