0=x^2-86x+840

Solution for 0=x^2-86x+840 equation:

0=x^2-86x+840

We move all terms to the left:

0-(x^2-86x+840)=0

We add all the numbers together, and all the variables

-(x^2-86x+840)=0

We get rid of parentheses

-x^2+86x-840=0

We add all the numbers together, and all the variables

-1x^2+86x-840=0

a = -1; b = 86; c = -840;
Δ = b2-4ac
Δ = 862-4·(-1)·(-840)
Δ = 4036
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:

$\sqrt{\Delta}=\sqrt{4036}=\sqrt{4*1009}=\sqrt{4}*\sqrt{1009}=2\sqrt{1009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-2\sqrt{1009}}{2*-1}=\frac{-86-2\sqrt{1009}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+2\sqrt{1009}}{2*-1}=\frac{-86+2\sqrt{1009}}{-2}
$