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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2-125x-25x+1=0

We add all the numbers together, and all the variables

15x^2-150x+1=0

a = 15; b = -150; c = +1;
Δ = b2-4ac
Δ = -1502-4·15·1
Δ = 22440
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:

$\sqrt{\Delta}=\sqrt{22440}=\sqrt{4*5610}=\sqrt{4}*\sqrt{5610}=2\sqrt{5610}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5610}}{2*15}=\frac{150-2\sqrt{5610}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5610}}{2*15}=\frac{150+2\sqrt{5610}}{30}
$