(x+5)(x-3)=105

Solution for (x+5)(x-3)=105 equation:

(x+5)(x-3)=105

We move all terms to the left:

(x+5)(x-3)-(105)=0

We multiply parentheses ..

(+x^2-3x+5x-15)-105=0

We get rid of parentheses

x^2-3x+5x-15-105=0

We add all the numbers together, and all the variables

x^2+2x-120=0

a = 1; b = 2; c = -120;
Δ = b2-4ac
Δ = 22-4·1·(-120)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*1}=\frac{20}{2}
=10
$