(-5/6)e-(2/3)e=-24

Solution for (-5/6)e-(2/3)e=-24 equation:

(-5/6)e-(2/3)e=-24

We move all terms to the left:

(-5/6)e-(2/3)e-(-24)=0


Domain of the equation: 6)e!=0

e!=0/1

e!=0

e∈R



Domain of the equation: 3)e!=0

e!=0/1

e!=0

e∈R


We add all the numbers together, and all the variables

(-5/6)e-(+2/3)e-(-24)=0

We add all the numbers together, and all the variables

(-5/6)e-(+2/3)e+24=0

We multiply parentheses

-5e^2-2e^2+24=0

We add all the numbers together, and all the variables

-7e^2+24=0

a = -7; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-7)·24
Δ = 672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*-7}=\frac{0-4\sqrt{42}}{-14}
=-\frac{4\sqrt{42}}{-14}
=-\frac{2\sqrt{42}}{-7}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*-7}=\frac{0+4\sqrt{42}}{-14}
=\frac{4\sqrt{42}}{-14}
=\frac{2\sqrt{42}}{-7}
$