76=x-1/5x

Solution for 76=x-1/5x equation:

76=x-1/5x

We move all terms to the left:

76-(x-1/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-1/5x)+76=0

We get rid of parentheses

-x+1/5x+76=0

We multiply all the terms by the denominator


-x*5x+76*5x+1=0

Wy multiply elements

-5x^2+380x+1=0

a = -5; b = 380; c = +1;
Δ = b2-4ac
Δ = 3802-4·(-5)·1
Δ = 144420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{144420}=\sqrt{4*36105}=\sqrt{4}*\sqrt{36105}=2\sqrt{36105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(380)-2\sqrt{36105}}{2*-5}=\frac{-380-2\sqrt{36105}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(380)+2\sqrt{36105}}{2*-5}=\frac{-380+2\sqrt{36105}}{-10}
$