45-42z-24z^2=0

Solution for 45-42z-24z^2=0 equation:

45-42z-24z^2=0

a = -24; b = -42; c = +45;
Δ = b2-4ac
Δ = -422-4·(-24)·45
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-78}{2*-24}=\frac{-36}{-48}
=3/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+78}{2*-24}=\frac{120}{-48}
=-2+1/2
$