42x2=84

Solution for 42x2=84 equation:

42x^2=84

We move all terms to the left:

42x^2-(84)=0

a = 42; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·42·(-84)
Δ = 14112
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:

$\sqrt{\Delta}=\sqrt{14112}=\sqrt{7056*2}=\sqrt{7056}*\sqrt{2}=84\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{2}}{2*42}=\frac{0-84\sqrt{2}}{84}
=-\frac{84\sqrt{2}}{84}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{2}}{2*42}=\frac{0+84\sqrt{2}}{84}
=\frac{84\sqrt{2}}{84}
=\sqrt{2}
$