(3x+1)(7x+11)=180

Solution for (3x+1)(7x+11)=180 equation:

(3x+1)(7x+11)=180

We move all terms to the left:

(3x+1)(7x+11)-(180)=0

We multiply parentheses ..

(+21x^2+33x+7x+11)-180=0

We get rid of parentheses

21x^2+33x+7x+11-180=0

We add all the numbers together, and all the variables

21x^2+40x-169=0

a = 21; b = 40; c = -169;
Δ = b2-4ac
Δ = 402-4·21·(-169)
Δ = 15796
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:

$\sqrt{\Delta}=\sqrt{15796}=\sqrt{4*3949}=\sqrt{4}*\sqrt{3949}=2\sqrt{3949}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{3949}}{2*21}=\frac{-40-2\sqrt{3949}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{3949}}{2*21}=\frac{-40+2\sqrt{3949}}{42}
$