(X+139)(x+57)=180

Solution for (X+139)(x+57)=180 equation:

(X+139)(X+57)=180

We move all terms to the left:

(X+139)(X+57)-(180)=0

We multiply parentheses ..

(+X^2+57X+139X+7923)-180=0

We get rid of parentheses

X^2+57X+139X+7923-180=0

We add all the numbers together, and all the variables

X^2+196X+7743=0

a = 1; b = 196; c = +7743;
Δ = b2-4ac
Δ = 1962-4·1·7743
Δ = 7444
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:

$\sqrt{\Delta}=\sqrt{7444}=\sqrt{4*1861}=\sqrt{4}*\sqrt{1861}=2\sqrt{1861}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-2\sqrt{1861}}{2*1}=\frac{-196-2\sqrt{1861}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+2\sqrt{1861}}{2*1}=\frac{-196+2\sqrt{1861}}{2}
$