6z^2+7z=77

Solution for 6z^2+7z=77 equation:

6z^2+7z=77

We move all terms to the left:

6z^2+7z-(77)=0

a = 6; b = 7; c = -77;
Δ = b2-4ac
Δ = 72-4·6·(-77)
Δ = 1897
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{-(7)-\sqrt{1897}}{2*6}=\frac{-7-\sqrt{1897}}{12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{1897}}{2*6}=\frac{-7+\sqrt{1897}}{12}
$