3z^2+5z+7=9

Solution for 3z^2+5z+7=9 equation:

3z^2+5z+7=9

We move all terms to the left:

3z^2+5z+7-(9)=0

We add all the numbers together, and all the variables

3z^2+5z-2=0

a = 3; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·3·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*3}=\frac{-12}{6}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*3}=\frac{2}{6}
=1/3
$