2x-40/x+7=360

Solution for 2x-40/x+7=360 equation:

2x-40/x+7=360

We move all terms to the left:

2x-40/x+7-(360)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-40/x-353=0

We multiply all the terms by the denominator


2x*x-353*x-40=0

We add all the numbers together, and all the variables

-353x+2x*x-40=0

Wy multiply elements

2x^2-353x-40=0

a = 2; b = -353; c = -40;
Δ = b2-4ac
Δ = -3532-4·2·(-40)
Δ = 124929
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:

$\sqrt{\Delta}=\sqrt{124929}=\sqrt{9*13881}=\sqrt{9}*\sqrt{13881}=3\sqrt{13881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-353)-3\sqrt{13881}}{2*2}=\frac{353-3\sqrt{13881}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-353)+3\sqrt{13881}}{2*2}=\frac{353+3\sqrt{13881}}{4}
$