7x+2/x=180

Solution for 7x+2/x=180 equation:

7x+2/x=180

We move all terms to the left:

7x+2/x-(180)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


7x*x-180*x+2=0

We add all the numbers together, and all the variables

-180x+7x*x+2=0

Wy multiply elements

7x^2-180x+2=0

a = 7; b = -180; c = +2;
Δ = b2-4ac
Δ = -1802-4·7·2
Δ = 32344
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:

$\sqrt{\Delta}=\sqrt{32344}=\sqrt{4*8086}=\sqrt{4}*\sqrt{8086}=2\sqrt{8086}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8086}}{2*7}=\frac{180-2\sqrt{8086}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8086}}{2*7}=\frac{180+2\sqrt{8086}}{14}
$