1/5x+4=25x-3

Solution for 1/5x+4=25x-3 equation:

1/5x+4=25x-3

We move all terms to the left:

1/5x+4-(25x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-25x+3+4=0

We multiply all the terms by the denominator


-25x*5x+3*5x+4*5x+1=0

Wy multiply elements

-125x^2+15x+20x+1=0

We add all the numbers together, and all the variables

-125x^2+35x+1=0

a = -125; b = 35; c = +1;
Δ = b2-4ac
Δ = 352-4·(-125)·1
Δ = 1725
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:

$\sqrt{\Delta}=\sqrt{1725}=\sqrt{25*69}=\sqrt{25}*\sqrt{69}=5\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5\sqrt{69}}{2*-125}=\frac{-35-5\sqrt{69}}{-250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{69}}{2*-125}=\frac{-35+5\sqrt{69}}{-250}
$