(X-77)(x-63)=300

Solution for (X-77)(x-63)=300 equation:

(X-77)(X-63)=300

We move all terms to the left:

(X-77)(X-63)-(300)=0

We multiply parentheses ..

(+X^2-63X-77X+4851)-300=0

We get rid of parentheses

X^2-63X-77X+4851-300=0

We add all the numbers together, and all the variables

X^2-140X+4551=0

a = 1; b = -140; c = +4551;
Δ = b2-4ac
Δ = -1402-4·1·4551
Δ = 1396
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:

$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{349}}{2*1}=\frac{140-2\sqrt{349}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{349}}{2*1}=\frac{140+2\sqrt{349}}{2}
$