(X-3)(x+4)=78

Solution for (X-3)(x+4)=78 equation:

(X-3)(X+4)=78

We move all terms to the left:

(X-3)(X+4)-(78)=0

We multiply parentheses ..

(+X^2+4X-3X-12)-78=0

We get rid of parentheses

X^2+4X-3X-12-78=0

We add all the numbers together, and all the variables

X^2+X-90=0

a = 1; b = 1; c = -90;
Δ = b2-4ac
Δ = 12-4·1·(-90)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-19}{2*1}=\frac{-20}{2}
=-10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*1}=\frac{18}{2}
=9
$