4/10x=5x-1

Solution for 4/10x=5x-1 equation:

4/10x=5x-1

We move all terms to the left:

4/10x-(5x-1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

4/10x-5x+1=0

We multiply all the terms by the denominator


-5x*10x+1*10x+4=0

Wy multiply elements

-50x^2+10x+4=0

a = -50; b = 10; c = +4;
Δ = b2-4ac
Δ = 102-4·(-50)·4
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*-50}=\frac{-40}{-100}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*-50}=\frac{20}{-100}
=-1/5
$