(X-37)(x-47)=296

Solution for (X-37)(x-47)=296 equation:

(X-37)(X-47)=296

We move all terms to the left:

(X-37)(X-47)-(296)=0

We multiply parentheses ..

(+X^2-47X-37X+1739)-296=0

We get rid of parentheses

X^2-47X-37X+1739-296=0

We add all the numbers together, and all the variables

X^2-84X+1443=0

a = 1; b = -84; c = +1443;
Δ = b2-4ac
Δ = -842-4·1·1443
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{321}}{2*1}=\frac{84-2\sqrt{321}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{321}}{2*1}=\frac{84+2\sqrt{321}}{2}
$