-8-2-7+1=1/4(20)e-e

Solution for -8-2-7+1=1/4(20)e-e equation:

-8-2-7+1=1/4(20)e-e

We move all terms to the left:

-8-2-7+1-(1/4(20)e-e)=0


Domain of the equation: 420e-e)!=0

e∈R


We add all the numbers together, and all the variables

-(-1e+1/420e)-8-2-7+1=0

We add all the numbers together, and all the variables

-(-1e+1/420e)-16=0

We get rid of parentheses

1e-1/420e-16=0

We multiply all the terms by the denominator


1e*420e-16*420e-1=0

Wy multiply elements

420e^2-6720e-1=0

a = 420; b = -6720; c = -1;
Δ = b2-4ac
Δ = -67202-4·420·(-1)
Δ = 45160080
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:

$\sqrt{\Delta}=\sqrt{45160080}=\sqrt{16*2822505}=\sqrt{16}*\sqrt{2822505}=4\sqrt{2822505}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6720)-4\sqrt{2822505}}{2*420}=\frac{6720-4\sqrt{2822505}}{840}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6720)+4\sqrt{2822505}}{2*420}=\frac{6720+4\sqrt{2822505}}{840}
$