2x-40/x+7=180

Solution for 2x-40/x+7=180 equation:

2x-40/x+7=180

We move all terms to the left:

2x-40/x+7-(180)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-40/x-173=0

We multiply all the terms by the denominator


2x*x-173*x-40=0

We add all the numbers together, and all the variables

-173x+2x*x-40=0

Wy multiply elements

2x^2-173x-40=0

a = 2; b = -173; c = -40;
Δ = b2-4ac
Δ = -1732-4·2·(-40)
Δ = 30249
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:

$\sqrt{\Delta}=\sqrt{30249}=\sqrt{9*3361}=\sqrt{9}*\sqrt{3361}=3\sqrt{3361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-173)-3\sqrt{3361}}{2*2}=\frac{173-3\sqrt{3361}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-173)+3\sqrt{3361}}{2*2}=\frac{173+3\sqrt{3361}}{4}
$