36.x^2-x=42

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

36.x^2-x=42

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = 36.; b = -1; c = -42;
Δ = b2-4ac
Δ = -12-4·36.·(-42)
Δ = 6049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{6049}}{2*36.}=\frac{1-\sqrt{6049}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{6049}}{2*36.}=\frac{1+\sqrt{6049}}{72}
$