(X-2)(x+3)=234

Solution for (X-2)(x+3)=234 equation:

(X-2)(X+3)=234

We move all terms to the left:

(X-2)(X+3)-(234)=0

We multiply parentheses ..

(+X^2+3X-2X-6)-234=0

We get rid of parentheses

X^2+3X-2X-6-234=0

We add all the numbers together, and all the variables

X^2+X-240=0

a = 1; b = 1; c = -240;
Δ = b2-4ac
Δ = 12-4·1·(-240)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*1}=\frac{-32}{2}
=-16
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*1}=\frac{30}{2}
=15
$