-1/5x+4=5x-22

Solution for -1/5x+4=5x-22 equation:

-1/5x+4=5x-22

We move all terms to the left:

-1/5x+4-(5x-22)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x-5x+22+4=0

We multiply all the terms by the denominator


-5x*5x+22*5x+4*5x-1=0

Wy multiply elements

-25x^2+110x+20x-1=0

We add all the numbers together, and all the variables

-25x^2+130x-1=0

a = -25; b = 130; c = -1;
Δ = b2-4ac
Δ = 1302-4·(-25)·(-1)
Δ = 16800
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:

$\sqrt{\Delta}=\sqrt{16800}=\sqrt{400*42}=\sqrt{400}*\sqrt{42}=20\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-20\sqrt{42}}{2*-25}=\frac{-130-20\sqrt{42}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+20\sqrt{42}}{2*-25}=\frac{-130+20\sqrt{42}}{-50}
$