(8x+11)(9x+9)=122

Solution for (8x+11)(9x+9)=122 equation:

(8x+11)(9x+9)=122

We move all terms to the left:

(8x+11)(9x+9)-(122)=0

We multiply parentheses ..

(+72x^2+72x+99x+99)-122=0

We get rid of parentheses

72x^2+72x+99x+99-122=0

We add all the numbers together, and all the variables

72x^2+171x-23=0

a = 72; b = 171; c = -23;
Δ = b2-4ac
Δ = 1712-4·72·(-23)
Δ = 35865
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:

$\sqrt{\Delta}=\sqrt{35865}=\sqrt{9*3985}=\sqrt{9}*\sqrt{3985}=3\sqrt{3985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(171)-3\sqrt{3985}}{2*72}=\frac{-171-3\sqrt{3985}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+3\sqrt{3985}}{2*72}=\frac{-171+3\sqrt{3985}}{144}
$