(3x+6)(4x-29)=180

Solution for (3x+6)(4x-29)=180 equation:

(3x+6)(4x-29)=180

We move all terms to the left:

(3x+6)(4x-29)-(180)=0

We multiply parentheses ..

(+12x^2-87x+24x-174)-180=0

We get rid of parentheses

12x^2-87x+24x-174-180=0

We add all the numbers together, and all the variables

12x^2-63x-354=0

a = 12; b = -63; c = -354;
Δ = b2-4ac
Δ = -632-4·12·(-354)
Δ = 20961
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:

$\sqrt{\Delta}=\sqrt{20961}=\sqrt{9*2329}=\sqrt{9}*\sqrt{2329}=3\sqrt{2329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{2329}}{2*12}=\frac{63-3\sqrt{2329}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{2329}}{2*12}=\frac{63+3\sqrt{2329}}{24}
$