(X+16)(x-6)=180

Solution for (X+16)(x-6)=180 equation:

(X+16)(X-6)=180

We move all terms to the left:

(X+16)(X-6)-(180)=0

We multiply parentheses ..

(+X^2-6X+16X-96)-180=0

We get rid of parentheses

X^2-6X+16X-96-180=0

We add all the numbers together, and all the variables

X^2+10X-276=0

a = 1; b = 10; c = -276;
Δ = b2-4ac
Δ = 102-4·1·(-276)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{301}}{2*1}=\frac{-10-2\sqrt{301}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{301}}{2*1}=\frac{-10+2\sqrt{301}}{2}
$