(x)=6x2+18x+3

Solution for (x)=6x2+18x+3 equation:

(x)=6x^2+18x+3

We move all terms to the left:

(x)-(6x^2+18x+3)=0

We get rid of parentheses

-6x^2+x-18x-3=0

We add all the numbers together, and all the variables

-6x^2-17x-3=0

a = -6; b = -17; c = -3;
Δ = b2-4ac
Δ = -172-4·(-6)·(-3)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{217}}{2*-6}=\frac{17-\sqrt{217}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{217}}{2*-6}=\frac{17+\sqrt{217}}{-12}
$