4/5x=10x+4

Solution for 4/5x=10x+4 equation:

4/5x=10x+4

We move all terms to the left:

4/5x-(10x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-10x-4=0

We multiply all the terms by the denominator


-10x*5x-4*5x+4=0

Wy multiply elements

-50x^2-20x+4=0

a = -50; b = -20; c = +4;
Δ = b2-4ac
Δ = -202-4·(-50)·4
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{3}}{2*-50}=\frac{20-20\sqrt{3}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{3}}{2*-50}=\frac{20+20\sqrt{3}}{-100}
$