(x+19)(x-2)=60

Solution for (x+19)(x-2)=60 equation:

(x+19)(x-2)=60

We move all terms to the left:

(x+19)(x-2)-(60)=0

We multiply parentheses ..

(+x^2-2x+19x-38)-60=0

We get rid of parentheses

x^2-2x+19x-38-60=0

We add all the numbers together, and all the variables

x^2+17x-98=0

a = 1; b = 17; c = -98;
Δ = b2-4ac
Δ = 172-4·1·(-98)
Δ = 681
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{-(17)-\sqrt{681}}{2*1}=\frac{-17-\sqrt{681}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{681}}{2*1}=\frac{-17+\sqrt{681}}{2}
$