(19-x)x-2=-10

Solution for (19-x)x-2=-10 equation:

(19-x)x-2=-10

We move all terms to the left:

(19-x)x-2-(-10)=0

We add all the numbers together, and all the variables

(-1x+19)x-2-(-10)=0

We add all the numbers together, and all the variables

(-1x+19)x+8=0

We multiply parentheses

-1x^2+19x+8=0

a = -1; b = 19; c = +8;
Δ = b2-4ac
Δ = 192-4·(-1)·8
Δ = 393
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{-(19)-\sqrt{393}}{2*-1}=\frac{-19-\sqrt{393}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{393}}{2*-1}=\frac{-19+\sqrt{393}}{-2}
$