42x^2-42=13

Solution for 42x^2-42=13 equation:

42x^2-42=13

We move all terms to the left:

42x^2-42-(13)=0

We add all the numbers together, and all the variables

42x^2-55=0

a = 42; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·42·(-55)
Δ = 9240
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:

$\sqrt{\Delta}=\sqrt{9240}=\sqrt{4*2310}=\sqrt{4}*\sqrt{2310}=2\sqrt{2310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2310}}{2*42}=\frac{0-2\sqrt{2310}}{84}
=-\frac{2\sqrt{2310}}{84}
=-\frac{\sqrt{2310}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2310}}{2*42}=\frac{0+2\sqrt{2310}}{84}
=\frac{2\sqrt{2310}}{84}
=\frac{\sqrt{2310}}{42}
$