7/9e+10-1/9e-8-2/3e=+5/3e

Solution for 7/9e+10-1/9e-8-2/3e=+5/3e equation:

7/9e+10-1/9e-8-2/3e=+5/3e

We move all terms to the left:

7/9e+10-1/9e-8-2/3e-(+5/3e)=0


Domain of the equation: 9e!=0

e!=0/9

e!=0

e∈R



Domain of the equation: 3e!=0

e!=0/3

e!=0

e∈R



Domain of the equation: 3e)!=0

e!=0/1

e!=0

e∈R


We add all the numbers together, and all the variables

7/9e-1/9e-2/3e-(+5/3e)+2=0

We get rid of parentheses

7/9e-1/9e-2/3e-5/3e+2=0

We calculate fractions


(-3e+7)/27e^2+(-45e-2)/27e^2+2=0

We multiply all the terms by the denominator


(-3e+7)+(-45e-2)+2*27e^2=0

Wy multiply elements

54e^2+(-3e+7)+(-45e-2)=0

We get rid of parentheses

54e^2-3e-45e+7-2=0

We add all the numbers together, and all the variables

54e^2-48e+5=0

a = 54; b = -48; c = +5;
Δ = b2-4ac
Δ = -482-4·54·5
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-6\sqrt{34}}{2*54}=\frac{48-6\sqrt{34}}{108}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+6\sqrt{34}}{2*54}=\frac{48+6\sqrt{34}}{108}
$