/5x=-2x+49

Solution for /5x=-2x+49 equation:

/5x=-2x+49

We move all terms to the left:

/5x-(-2x+49)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

/5x+2x-49=0

We multiply all the terms by the denominator


2x*5x-49*5x+=0

We add all the numbers together, and all the variables

2x*5x-49*5x=0

Wy multiply elements

10x^2-245x=0

a = 10; b = -245; c = 0;
Δ = b2-4ac
Δ = -2452-4·10·0
Δ = 60025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{60025}=245$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-245)-245}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-245)+245}{2*10}=\frac{490}{20}
=24+1/2
$