x+7/x=10

Solution for x+7/x=10 equation:

x+7/x=10

We move all terms to the left:

x+7/x-(10)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-10*x+7=0

We add all the numbers together, and all the variables

-10x+x*x+7=0

Wy multiply elements

x^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}
$