42x^2-53=x

Solution for 42x^2-53=x equation:

42x^2-53=x

We move all terms to the left:

42x^2-53-(x)=0

We add all the numbers together, and all the variables

42x^2-1x-53=0

a = 42; b = -1; c = -53;
Δ = b2-4ac
Δ = -12-4·42·(-53)
Δ = 8905
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{8905}}{2*42}=\frac{1-\sqrt{8905}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{8905}}{2*42}=\frac{1+\sqrt{8905}}{84}
$