6z*z+23z=18

Solution for 6z*z+23z=18 equation:

6z*z+23z=18

We move all terms to the left:

6z*z+23z-(18)=0

We add all the numbers together, and all the variables

23z+6z*z-18=0

Wy multiply elements

6z^2+23z-18=0

a = 6; b = 23; c = -18;
Δ = b2-4ac
Δ = 232-4·6·(-18)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-31}{2*6}=\frac{-54}{12}
=-4+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+31}{2*6}=\frac{8}{12}
=2/3
$