5z^2+30z=123

Solution for 5z^2+30z=123 equation:

5z^2+30z=123

We move all terms to the left:

5z^2+30z-(123)=0

a = 5; b = 30; c = -123;
Δ = b2-4ac
Δ = 302-4·5·(-123)
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{210}}{2*5}=\frac{-30-4\sqrt{210}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{210}}{2*5}=\frac{-30+4\sqrt{210}}{10}
$