43z-5z^2=24

Solution for 43z-5z^2=24 equation:

43z-5z^2=24

We move all terms to the left:

43z-5z^2-(24)=0

a = -5; b = 43; c = -24;
Δ = b2-4ac
Δ = 432-4·(-5)·(-24)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-37}{2*-5}=\frac{-80}{-10}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+37}{2*-5}=\frac{-6}{-10}
=3/5
$