(16x+4)(3x+11)=110

Solution for (16x+4)(3x+11)=110 equation:

(16x+4)(3x+11)=110

We move all terms to the left:

(16x+4)(3x+11)-(110)=0

We multiply parentheses ..

(+48x^2+176x+12x+44)-110=0

We get rid of parentheses

48x^2+176x+12x+44-110=0

We add all the numbers together, and all the variables

48x^2+188x-66=0

a = 48; b = 188; c = -66;
Δ = b2-4ac
Δ = 1882-4·48·(-66)
Δ = 48016
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:

$\sqrt{\Delta}=\sqrt{48016}=\sqrt{16*3001}=\sqrt{16}*\sqrt{3001}=4\sqrt{3001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(188)-4\sqrt{3001}}{2*48}=\frac{-188-4\sqrt{3001}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(188)+4\sqrt{3001}}{2*48}=\frac{-188+4\sqrt{3001}}{96}
$