(12x+1)(+7x+8)=180

Solution for (12x+1)(+7x+8)=180 equation:

(12x+1)(+7x+8)=180

We move all terms to the left:

(12x+1)(+7x+8)-(180)=0

We add all the numbers together, and all the variables

(12x+1)(7x+8)-180=0

We multiply parentheses ..

(+84x^2+96x+7x+8)-180=0

We get rid of parentheses

84x^2+96x+7x+8-180=0

We add all the numbers together, and all the variables

84x^2+103x-172=0

a = 84; b = 103; c = -172;
Δ = b2-4ac
Δ = 1032-4·84·(-172)
Δ = 68401
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{-(103)-\sqrt{68401}}{2*84}=\frac{-103-\sqrt{68401}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+\sqrt{68401}}{2*84}=\frac{-103+\sqrt{68401}}{168}
$