(6x+-1)(7x+1)=180

Solution for (6x+-1)(7x+1)=180 equation:

(6x+-1)(7x+1)=180

We move all terms to the left:

(6x+-1)(7x+1)-(180)=0

We add all the numbers together, and all the variables

(6x-1)(7x+1)-180=0

We multiply parentheses ..

(+42x^2+6x-7x-1)-180=0

We get rid of parentheses

42x^2+6x-7x-1-180=0

We add all the numbers together, and all the variables

42x^2-1x-181=0

a = 42; b = -1; c = -181;
Δ = b2-4ac
Δ = -12-4·42·(-181)
Δ = 30409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{30409}}{2*42}=\frac{1-\sqrt{30409}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{30409}}{2*42}=\frac{1+\sqrt{30409}}{84}
$