0=x^2-42x-36

Solution for 0=x^2-42x-36 equation:

0=x^2-42x-36

We move all terms to the left:

0-(x^2-42x-36)=0

We add all the numbers together, and all the variables

-(x^2-42x-36)=0

We get rid of parentheses

-x^2+42x+36=0

We add all the numbers together, and all the variables

-1x^2+42x+36=0

a = -1; b = 42; c = +36;
Δ = b2-4ac
Δ = 422-4·(-1)·36
Δ = 1908
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:

$\sqrt{\Delta}=\sqrt{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{53}}{2*-1}=\frac{-42-6\sqrt{53}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{53}}{2*-1}=\frac{-42+6\sqrt{53}}{-2}
$