2x(3x+1)=26

Solution for 2x(3x+1)=26 equation:

2x(3x+1)=26

We move all terms to the left:

2x(3x+1)-(26)=0

We multiply parentheses

6x^2+2x-26=0

a = 6; b = 2; c = -26;
Δ = b2-4ac
Δ = 22-4·6·(-26)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{157}}{2*6}=\frac{-2-2\sqrt{157}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{157}}{2*6}=\frac{-2+2\sqrt{157}}{12}
$