6-(3x+1)*(3x+1)=-30

Solution for 6-(3x+1)*(3x+1)=-30 equation:

6-(3x+1)(3x+1)=-30

We move all terms to the left:

6-(3x+1)(3x+1)-(-30)=0

We add all the numbers together, and all the variables

-(3x+1)(3x+1)+36=0

We multiply parentheses ..

-(+9x^2+3x+3x+1)+36=0

We get rid of parentheses

-9x^2-3x-3x-1+36=0

We add all the numbers together, and all the variables

-9x^2-6x+35=0

a = -9; b = -6; c = +35;
Δ = b2-4ac
Δ = -62-4·(-9)·35
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-36}{2*-9}=\frac{-30}{-18}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+36}{2*-9}=\frac{42}{-18}
=-2+1/3
$