6z^2+3z=5

Solution for 6z^2+3z=5 equation:

6z^2+3z=5

We move all terms to the left:

6z^2+3z-(5)=0

a = 6; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·6·(-5)
Δ = 129
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{-(3)-\sqrt{129}}{2*6}=\frac{-3-\sqrt{129}}{12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{129}}{2*6}=\frac{-3+\sqrt{129}}{12}
$