(3z-1)(2z+3)=94

Solution for (3z-1)(2z+3)=94 equation:

(3z-1)(2z+3)=94

We move all terms to the left:

(3z-1)(2z+3)-(94)=0

We multiply parentheses ..

(+6z^2+9z-2z-3)-94=0

We get rid of parentheses

6z^2+9z-2z-3-94=0

We add all the numbers together, and all the variables

6z^2+7z-97=0

a = 6; b = 7; c = -97;
Δ = b2-4ac
Δ = 72-4·6·(-97)
Δ = 2377
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{2377}}{2*6}=\frac{-7-\sqrt{2377}}{12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{2377}}{2*6}=\frac{-7+\sqrt{2377}}{12}
$