(X-2)(x+3)=13

Solution for (X-2)(x+3)=13 equation:

(X-2)(X+3)=13

We move all terms to the left:

(X-2)(X+3)-(13)=0

We multiply parentheses ..

(+X^2+3X-2X-6)-13=0

We get rid of parentheses

X^2+3X-2X-6-13=0

We add all the numbers together, and all the variables

X^2+X-19=0

a = 1; b = 1; c = -19;
Δ = b2-4ac
Δ = 12-4·1·(-19)
Δ = 77
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{-(1)-\sqrt{77}}{2*1}=\frac{-1-\sqrt{77}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{77}}{2*1}=\frac{-1+\sqrt{77}}{2}
$