7z^2=1526

Solution for 7z^2=1526 equation:

7z^2=1526

We move all terms to the left:

7z^2-(1526)=0

a = 7; b = 0; c = -1526;
Δ = b2-4ac
Δ = 02-4·7·(-1526)
Δ = 42728
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:

$\sqrt{\Delta}=\sqrt{42728}=\sqrt{196*218}=\sqrt{196}*\sqrt{218}=14\sqrt{218}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{218}}{2*7}=\frac{0-14\sqrt{218}}{14}
=-\frac{14\sqrt{218}}{14}
=-\sqrt{218}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{218}}{2*7}=\frac{0+14\sqrt{218}}{14}
=\frac{14\sqrt{218}}{14}
=\sqrt{218}
$