(3x+8)(6x+1)=180

Solution for (3x+8)(6x+1)=180 equation:

(3x+8)(6x+1)=180

We move all terms to the left:

(3x+8)(6x+1)-(180)=0

We multiply parentheses ..

(+18x^2+3x+48x+8)-180=0

We get rid of parentheses

18x^2+3x+48x+8-180=0

We add all the numbers together, and all the variables

18x^2+51x-172=0

a = 18; b = 51; c = -172;
Δ = b2-4ac
Δ = 512-4·18·(-172)
Δ = 14985
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:

$\sqrt{\Delta}=\sqrt{14985}=\sqrt{81*185}=\sqrt{81}*\sqrt{185}=9\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-9\sqrt{185}}{2*18}=\frac{-51-9\sqrt{185}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+9\sqrt{185}}{2*18}=\frac{-51+9\sqrt{185}}{36}
$