(3x+29)(6x-3)+37=180

Solution for (3x+29)(6x-3)+37=180 equation:

(3x+29)(6x-3)+37=180

We move all terms to the left:

(3x+29)(6x-3)+37-(180)=0

We add all the numbers together, and all the variables

(3x+29)(6x-3)-143=0

We multiply parentheses ..

(+18x^2-9x+174x-87)-143=0

We get rid of parentheses

18x^2-9x+174x-87-143=0

We add all the numbers together, and all the variables

18x^2+165x-230=0

a = 18; b = 165; c = -230;
Δ = b2-4ac
Δ = 1652-4·18·(-230)
Δ = 43785
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:

$\sqrt{\Delta}=\sqrt{43785}=\sqrt{9*4865}=\sqrt{9}*\sqrt{4865}=3\sqrt{4865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(165)-3\sqrt{4865}}{2*18}=\frac{-165-3\sqrt{4865}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(165)+3\sqrt{4865}}{2*18}=\frac{-165+3\sqrt{4865}}{36}
$