5x+7=72/x+1

Solution for 5x+7=72/x+1 equation:

5x+7=72/x+1

We move all terms to the left:

5x+7-(72/x+1)=0


Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

5x-72/x-1+7=0

We multiply all the terms by the denominator


5x*x-1*x+7*x-72=0

We add all the numbers together, and all the variables

6x+5x*x-72=0

Wy multiply elements

5x^2+6x-72=0

a = 5; b = 6; c = -72;
Δ = b2-4ac
Δ = 62-4·5·(-72)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{41}}{2*5}=\frac{-6-6\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{41}}{2*5}=\frac{-6+6\sqrt{41}}{10}
$