(X+14)(4x-9)=180

Solution for (X+14)(4x-9)=180 equation:

(X+14)(4X-9)=180

We move all terms to the left:

(X+14)(4X-9)-(180)=0

We multiply parentheses ..

(+4X^2-9X+56X-126)-180=0

We get rid of parentheses

4X^2-9X+56X-126-180=0

We add all the numbers together, and all the variables

4X^2+47X-306=0

a = 4; b = 47; c = -306;
Δ = b2-4ac
Δ = 472-4·4·(-306)
Δ = 7105
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:

$\sqrt{\Delta}=\sqrt{7105}=\sqrt{49*145}=\sqrt{49}*\sqrt{145}=7\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-7\sqrt{145}}{2*4}=\frac{-47-7\sqrt{145}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+7\sqrt{145}}{2*4}=\frac{-47+7\sqrt{145}}{8}
$