8z^2+6z^2+38=180

Solution for 8z^2+6z^2+38=180 equation:

8z^2+6z^2+38=180

We move all terms to the left:

8z^2+6z^2+38-(180)=0

We add all the numbers together, and all the variables

14z^2-142=0

a = 14; b = 0; c = -142;
Δ = b2-4ac
Δ = 02-4·14·(-142)
Δ = 7952
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:

$\sqrt{\Delta}=\sqrt{7952}=\sqrt{16*497}=\sqrt{16}*\sqrt{497}=4\sqrt{497}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{497}}{2*14}=\frac{0-4\sqrt{497}}{28}
=-\frac{4\sqrt{497}}{28}
=-\frac{\sqrt{497}}{7}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{497}}{2*14}=\frac{0+4\sqrt{497}}{28}
=\frac{4\sqrt{497}}{28}
=\frac{\sqrt{497}}{7}
$