x(3x+26)=-6

Solution for x(3x+26)=-6 equation:

x(3x+26)=-6

We move all terms to the left:

x(3x+26)-(-6)=0

We add all the numbers together, and all the variables

x(3x+26)+6=0

We multiply parentheses

3x^2+26x+6=0

a = 3; b = 26; c = +6;
Δ = b2-4ac
Δ = 262-4·3·6
Δ = 604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{151}}{2*3}=\frac{-26-2\sqrt{151}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{151}}{2*3}=\frac{-26+2\sqrt{151}}{6}
$