(X+12)(4x-7)=180

Solution for (X+12)(4x-7)=180 equation:

(X+12)(4X-7)=180

We move all terms to the left:

(X+12)(4X-7)-(180)=0

We multiply parentheses ..

(+4X^2-7X+48X-84)-180=0

We get rid of parentheses

4X^2-7X+48X-84-180=0

We add all the numbers together, and all the variables

4X^2+41X-264=0

a = 4; b = 41; c = -264;
Δ = b2-4ac
Δ = 412-4·4·(-264)
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{-(41)-\sqrt{5905}}{2*4}=\frac{-41-\sqrt{5905}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{5905}}{2*4}=\frac{-41+\sqrt{5905}}{8}
$