x+2/x+15=375

Solution for x+2/x+15=375 equation:

x+2/x+15=375

We move all terms to the left:

x+2/x+15-(375)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+2/x-360=0

We multiply all the terms by the denominator


x*x-360*x+2=0

We add all the numbers together, and all the variables

-360x+x*x+2=0

Wy multiply elements

x^2-360x+2=0

a = 1; b = -360; c = +2;
Δ = b2-4ac
Δ = -3602-4·1·2
Δ = 129592
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:

$\sqrt{\Delta}=\sqrt{129592}=\sqrt{4*32398}=\sqrt{4}*\sqrt{32398}=2\sqrt{32398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32398}}{2*1}=\frac{360-2\sqrt{32398}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32398}}{2*1}=\frac{360+2\sqrt{32398}}{2}
$