18-(x-86)(x-4)=19

Solution for 18-(x-86)(x-4)=19 equation:

18-(x-86)(x-4)=19

We move all terms to the left:

18-(x-86)(x-4)-(19)=0

We add all the numbers together, and all the variables

-(x-86)(x-4)-1=0

We multiply parentheses ..

-(+x^2-4x-86x+344)-1=0

We get rid of parentheses

-x^2+4x+86x-344-1=0

We add all the numbers together, and all the variables

-1x^2+90x-345=0

a = -1; b = 90; c = -345;
Δ = b2-4ac
Δ = 902-4·(-1)·(-345)
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-8\sqrt{105}}{2*-1}=\frac{-90-8\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+8\sqrt{105}}{2*-1}=\frac{-90+8\sqrt{105}}{-2}
$