42z^2=144

Solution for 42z^2=144 equation:

42z^2=144

We move all terms to the left:

42z^2-(144)=0

a = 42; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·42·(-144)
Δ = 24192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24192}=\sqrt{576*42}=\sqrt{576}*\sqrt{42}=24\sqrt{42}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{42}}{2*42}=\frac{0-24\sqrt{42}}{84}
=-\frac{24\sqrt{42}}{84}
=-\frac{2\sqrt{42}}{7}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{42}}{2*42}=\frac{0+24\sqrt{42}}{84}
=\frac{24\sqrt{42}}{84}
=\frac{2\sqrt{42}}{7}
$