(4x+1)(x+14)=180

Solution for (4x+1)(x+14)=180 equation:

(4x+1)(x+14)=180

We move all terms to the left:

(4x+1)(x+14)-(180)=0

We multiply parentheses ..

(+4x^2+56x+x+14)-180=0

We get rid of parentheses

4x^2+56x+x+14-180=0

We add all the numbers together, and all the variables

4x^2+57x-166=0

a = 4; b = 57; c = -166;
Δ = b2-4ac
Δ = 572-4·4·(-166)
Δ = 5905
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{-(57)-\sqrt{5905}}{2*4}=\frac{-57-\sqrt{5905}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+\sqrt{5905}}{2*4}=\frac{-57+\sqrt{5905}}{8}
$