-1/5x+100=-2x+10

Solution for -1/5x+100=-2x+10 equation:

-1/5x+100=-2x+10

We move all terms to the left:

-1/5x+100-(-2x+10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x+2x-10+100=0

We multiply all the terms by the denominator


2x*5x-10*5x+100*5x-1=0

Wy multiply elements

10x^2-50x+500x-1=0

We add all the numbers together, and all the variables

10x^2+450x-1=0

a = 10; b = 450; c = -1;
Δ = b2-4ac
Δ = 4502-4·10·(-1)
Δ = 202540
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:

$\sqrt{\Delta}=\sqrt{202540}=\sqrt{4*50635}=\sqrt{4}*\sqrt{50635}=2\sqrt{50635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-2\sqrt{50635}}{2*10}=\frac{-450-2\sqrt{50635}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+2\sqrt{50635}}{2*10}=\frac{-450+2\sqrt{50635}}{20}
$