5/12e+4e-6e-5=15

Solution for 5/12e+4e-6e-5=15 equation:

5/12e+4e-6e-5=15

We move all terms to the left:

5/12e+4e-6e-5-(15)=0


Domain of the equation: 12e!=0

e!=0/12

e!=0

e∈R


We add all the numbers together, and all the variables

-2e+5/12e-20=0

We multiply all the terms by the denominator


-2e*12e-20*12e+5=0

Wy multiply elements

-24e^2-240e+5=0

a = -24; b = -240; c = +5;
Δ = b2-4ac
Δ = -2402-4·(-24)·5
Δ = 58080
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:

$\sqrt{\Delta}=\sqrt{58080}=\sqrt{1936*30}=\sqrt{1936}*\sqrt{30}=44\sqrt{30}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-44\sqrt{30}}{2*-24}=\frac{240-44\sqrt{30}}{-48}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+44\sqrt{30}}{2*-24}=\frac{240+44\sqrt{30}}{-48}
$