(x+2)(11x+2)=144

Solution for (x+2)(11x+2)=144 equation:

(x+2)(11x+2)=144

We move all terms to the left:

(x+2)(11x+2)-(144)=0

We multiply parentheses ..

(+11x^2+2x+22x+4)-144=0

We get rid of parentheses

11x^2+2x+22x+4-144=0

We add all the numbers together, and all the variables

11x^2+24x-140=0

a = 11; b = 24; c = -140;
Δ = b2-4ac
Δ = 242-4·11·(-140)
Δ = 6736
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:

$\sqrt{\Delta}=\sqrt{6736}=\sqrt{16*421}=\sqrt{16}*\sqrt{421}=4\sqrt{421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{421}}{2*11}=\frac{-24-4\sqrt{421}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{421}}{2*11}=\frac{-24+4\sqrt{421}}{22}
$