10-x=7/x

Solution for 10-x=7/x equation:

10-x=7/x

We move all terms to the left:

10-x-(7/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+7/x)+10=0

We add all the numbers together, and all the variables

-1x-(+7/x)+10=0

We get rid of parentheses

-1x-7/x+10=0

We multiply all the terms by the denominator


-1x*x+10*x-7=0

We add all the numbers together, and all the variables

10x-1x*x-7=0

Wy multiply elements

-1x^2+10x-7=0

a = -1; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·(-1)·(-7)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{2}}{2*-1}=\frac{-10-6\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{2}}{2*-1}=\frac{-10+6\sqrt{2}}{-2}
$