(X-5)(x+2)=55

Solution for (X-5)(x+2)=55 equation:

(X-5)(X+2)=55

We move all terms to the left:

(X-5)(X+2)-(55)=0

We multiply parentheses ..

(+X^2+2X-5X-10)-55=0

We get rid of parentheses

X^2+2X-5X-10-55=0

We add all the numbers together, and all the variables

X^2-3X-65=0

a = 1; b = -3; c = -65;
Δ = b2-4ac
Δ = -32-4·1·(-65)
Δ = 269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{269}}{2*1}=\frac{3-\sqrt{269}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{269}}{2*1}=\frac{3+\sqrt{269}}{2}
$