1/7x=0.25x-2.75

Solution for 1/7x=0.25x-2.75 equation:

1/7x=0.25x-2.75

We move all terms to the left:

1/7x-(0.25x-2.75)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

1/7x-0.25x+2.75=0

We multiply all the terms by the denominator


-(0.25x)*7x+(2.75)*7x+1=0

We add all the numbers together, and all the variables

-(+0.25x)*7x+(2.75)*7x+1=0

We multiply parentheses

-0x^2+19.25x+1=0

We add all the numbers together, and all the variables

-1x^2+19.25x+1=0

a = -1; b = 19.25; c = +1;
Δ = b2-4ac
Δ = 19.252-4·(-1)·1
Δ = 374.5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19.25)-\sqrt{374.5625}}{2*-1}=\frac{-19.25-\sqrt{374.5625}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19.25)+\sqrt{374.5625}}{2*-1}=\frac{-19.25+\sqrt{374.5625}}{-2}
$