(x+7)(x-3)=119

Solution for (x+7)(x-3)=119 equation:

(x+7)(x-3)=119

We move all terms to the left:

(x+7)(x-3)-(119)=0

We multiply parentheses ..

(+x^2-3x+7x-21)-119=0

We get rid of parentheses

x^2-3x+7x-21-119=0

We add all the numbers together, and all the variables

x^2+4x-140=0

a = 1; b = 4; c = -140;
Δ = b2-4ac
Δ = 42-4·1·(-140)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-24}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+24}{2*1}=\frac{20}{2}
=10
$