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 = 17000
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:

$\sqrt{\Delta}=\sqrt{17000}=\sqrt{100*170}=\sqrt{100}*\sqrt{170}=10\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-10\sqrt{170}}{2*-25}=\frac{-130-10\sqrt{170}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+10\sqrt{170}}{2*-25}=\frac{-130+10\sqrt{170}}{-50}
$