(12x-29)(4x+1)=180

Solution for (12x-29)(4x+1)=180 equation:

(12x-29)(4x+1)=180

We move all terms to the left:

(12x-29)(4x+1)-(180)=0

We multiply parentheses ..

(+48x^2+12x-116x-29)-180=0

We get rid of parentheses

48x^2+12x-116x-29-180=0

We add all the numbers together, and all the variables

48x^2-104x-209=0

a = 48; b = -104; c = -209;
Δ = b2-4ac
Δ = -1042-4·48·(-209)
Δ = 50944
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:

$\sqrt{\Delta}=\sqrt{50944}=\sqrt{256*199}=\sqrt{256}*\sqrt{199}=16\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-16\sqrt{199}}{2*48}=\frac{104-16\sqrt{199}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+16\sqrt{199}}{2*48}=\frac{104+16\sqrt{199}}{96}
$