-24(4z-1)=39z(+2)

Solution for -24(4z-1)=39z(+2) equation:

-24(4z-1)=39z(+2)

We move all terms to the left:

-24(4z-1)-(39z(+2))=0

We add all the numbers together, and all the variables

-24(4z-1)-(39z2)=0

We add all the numbers together, and all the variables

-39z^2-24(4z-1)=0

We multiply parentheses

-39z^2-96z+24=0

a = -39; b = -96; c = +24;
Δ = b2-4ac
Δ = -962-4·(-39)·24
Δ = 12960
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:

$\sqrt{\Delta}=\sqrt{12960}=\sqrt{1296*10}=\sqrt{1296}*\sqrt{10}=36\sqrt{10}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-36\sqrt{10}}{2*-39}=\frac{96-36\sqrt{10}}{-78}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+36\sqrt{10}}{2*-39}=\frac{96+36\sqrt{10}}{-78}
$