7/x=(x-2)/5

Solution for 7/x=(x-2)/5 equation:

7/x=(x-2)/5

We move all terms to the left:

7/x-((x-2)/5)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


()/5x^2+(-((x-2)*x)/5x^2=0

We multiply all the terms by the denominator


(-((x-2)*x)+()=0


We calculate terms in parentheses: +(-((x-2)*x)+(), so:

-((x-2)*x)+(

We add all the numbers together, and all the variables

-((x-2)*x)


We calculate terms in parentheses: -((x-2)*x), so:

(x-2)*x

We multiply parentheses

x^2-2x

Back to the equation:

-(x^2-2x)


We get rid of parentheses

-x^2+2x

We add all the numbers together, and all the variables

-1x^2+2x

Back to the equation:

+(-1x^2+2x)


We get rid of parentheses

-1x^2+2x=0

a = -1; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-1}=\frac{0}{-2}
=0
$