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)=0

We get rid of parentheses

1e-1/420e=0

We multiply all the terms by the denominator


1e*420e-1=0

Wy multiply elements

420e^2-1=0

a = 420; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·420·(-1)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*420}=\frac{0-4\sqrt{105}}{840}
=-\frac{4\sqrt{105}}{840}
=-\frac{\sqrt{105}}{210}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*420}=\frac{0+4\sqrt{105}}{840}
=\frac{4\sqrt{105}}{840}
=\frac{\sqrt{105}}{210}
$