8z^2-13z=5

Solution for 8z^2-13z=5 equation:

8z^2-13z=5

We move all terms to the left:

8z^2-13z-(5)=0

a = 8; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·8·(-5)
Δ = 329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{329}}{2*8}=\frac{13-\sqrt{329}}{16}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{329}}{2*8}=\frac{13+\sqrt{329}}{16}
$