z(3z+14)=90

Solution for z(3z+14)=90 equation:

z(3z+14)=90

We move all terms to the left:

z(3z+14)-(90)=0

We multiply parentheses

3z^2+14z-90=0

a = 3; b = 14; c = -90;
Δ = b2-4ac
Δ = 142-4·3·(-90)
Δ = 1276
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:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{319}}{2*3}=\frac{-14-2\sqrt{319}}{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{319}}{2*3}=\frac{-14+2\sqrt{319}}{6}
$