3e-18=4-3-3/4e

Solution for 3e-18=4-3-3/4e equation:

3e-18=4-3-3/4e

We move all terms to the left:

3e-18-(4-3-3/4e)=0


Domain of the equation: 4e)!=0

e!=0/1

e!=0

e∈R


We add all the numbers together, and all the variables

3e-(-3/4e+1)-18=0

We get rid of parentheses

3e+3/4e-1-18=0

We multiply all the terms by the denominator


3e*4e-1*4e-18*4e+3=0

Wy multiply elements

12e^2-4e-72e+3=0

We add all the numbers together, and all the variables

12e^2-76e+3=0

a = 12; b = -76; c = +3;
Δ = b2-4ac
Δ = -762-4·12·3
Δ = 5632
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:

$\sqrt{\Delta}=\sqrt{5632}=\sqrt{256*22}=\sqrt{256}*\sqrt{22}=16\sqrt{22}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-16\sqrt{22}}{2*12}=\frac{76-16\sqrt{22}}{24}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+16\sqrt{22}}{2*12}=\frac{76+16\sqrt{22}}{24}
$