(24m-16)(-1/2)=30

Solution for (24m-16)(-1/2)=30 equation:

(24m-16)(-1/2)=30

We move all terms to the left:

(24m-16)(-1/2)-(30)=0

We multiply parentheses ..

(-24m^2-16*-1/2)-30=0

We multiply all the terms by the denominator


(-24m^2-16*-1-30*2)=0

We get rid of parentheses

-24m^2-1-16*-30*2=0

We add all the numbers together, and all the variables

-24m^2+959=0

a = -24; b = 0; c = +959;
Δ = b2-4ac
Δ = 02-4·(-24)·959
Δ = 92064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92064}=\sqrt{16*5754}=\sqrt{16}*\sqrt{5754}=4\sqrt{5754}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5754}}{2*-24}=\frac{0-4\sqrt{5754}}{-48}
=-\frac{4\sqrt{5754}}{-48}
=-\frac{\sqrt{5754}}{-12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5754}}{2*-24}=\frac{0+4\sqrt{5754}}{-48}
=\frac{4\sqrt{5754}}{-48}
=\frac{\sqrt{5754}}{-12}
$