72=x+5/7x

Solution for 72=x+5/7x equation:

72=x+5/7x

We move all terms to the left:

72-(x+5/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+5/7x)+72=0

We get rid of parentheses

-x-5/7x+72=0

We multiply all the terms by the denominator


-x*7x+72*7x-5=0

Wy multiply elements

-7x^2+504x-5=0

a = -7; b = 504; c = -5;
Δ = b2-4ac
Δ = 5042-4·(-7)·(-5)
Δ = 253876
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:

$\sqrt{\Delta}=\sqrt{253876}=\sqrt{4*63469}=\sqrt{4}*\sqrt{63469}=2\sqrt{63469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(504)-2\sqrt{63469}}{2*-7}=\frac{-504-2\sqrt{63469}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(504)+2\sqrt{63469}}{2*-7}=\frac{-504+2\sqrt{63469}}{-14}
$