-3z^2=9z-7

Solution for -3z^2=9z-7 equation:

-3z^2=9z-7

We move all terms to the left:

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

We get rid of parentheses

-3z^2-9z+7=0

a = -3; b = -9; c = +7;
Δ = b2-4ac
Δ = -92-4·(-3)·7
Δ = 165
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{-(-9)-\sqrt{165}}{2*-3}=\frac{9-\sqrt{165}}{-6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{165}}{2*-3}=\frac{9+\sqrt{165}}{-6}
$