15z+7z^2=18

Solution for 15z+7z^2=18 equation:

15z+7z^2=18

We move all terms to the left:

15z+7z^2-(18)=0

a = 7; b = 15; c = -18;
Δ = b2-4ac
Δ = 152-4·7·(-18)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-27}{2*7}=\frac{-42}{14}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+27}{2*7}=\frac{12}{14}
=6/7
$