(x+44)(7x-248)=180

Solution for (x+44)(7x-248)=180 equation:

(x+44)(7x-248)=180

We move all terms to the left:

(x+44)(7x-248)-(180)=0

We multiply parentheses ..

(+7x^2-248x+308x-10912)-180=0

We get rid of parentheses

7x^2-248x+308x-10912-180=0

We add all the numbers together, and all the variables

7x^2+60x-11092=0

a = 7; b = 60; c = -11092;
Δ = b2-4ac
Δ = 602-4·7·(-11092)
Δ = 314176
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:

$\sqrt{\Delta}=\sqrt{314176}=\sqrt{64*4909}=\sqrt{64}*\sqrt{4909}=8\sqrt{4909}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{4909}}{2*7}=\frac{-60-8\sqrt{4909}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{4909}}{2*7}=\frac{-60+8\sqrt{4909}}{14}
$