0=x^2-22x+84

Solution for 0=x^2-22x+84 equation:

0=x^2-22x+84

We move all terms to the left:

0-(x^2-22x+84)=0

We add all the numbers together, and all the variables

-(x^2-22x+84)=0

We get rid of parentheses

-x^2+22x-84=0

We add all the numbers together, and all the variables

-1x^2+22x-84=0

a = -1; b = 22; c = -84;
Δ = b2-4ac
Δ = 222-4·(-1)·(-84)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{37}}{2*-1}=\frac{-22-2\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{37}}{2*-1}=\frac{-22+2\sqrt{37}}{-2}
$