1/5x+8=25x+10

Solution for 1/5x+8=25x+10 equation:

1/5x+8=25x+10

We move all terms to the left:

1/5x+8-(25x+10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-25x-10+8=0

We multiply all the terms by the denominator


-25x*5x-10*5x+8*5x+1=0

Wy multiply elements

-125x^2-50x+40x+1=0

We add all the numbers together, and all the variables

-125x^2-10x+1=0

a = -125; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-125)·1
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{6}}{2*-125}=\frac{10-10\sqrt{6}}{-250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{6}}{2*-125}=\frac{10+10\sqrt{6}}{-250}
$