4-x(x-5)=x-19

Solution for 4-x(x-5)=x-19 equation:

4-x(x-5)=x-19

We move all terms to the left:

4-x(x-5)-(x-19)=0

We multiply parentheses

-x^2+5x-(x-19)+4=0

We get rid of parentheses

-x^2+5x-x+19+4=0

We add all the numbers together, and all the variables

-1x^2+4x+23=0

a = -1; b = 4; c = +23;
Δ = b2-4ac
Δ = 42-4·(-1)·23
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{3}}{2*-1}=\frac{-4-6\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{3}}{2*-1}=\frac{-4+6\sqrt{3}}{-2}
$