2x+15=385/x+1

Solution for 2x+15=385/x+1 equation:

2x+15=385/x+1

We move all terms to the left:

2x+15-(385/x+1)=0


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

x∈R


We get rid of parentheses

2x-385/x-1+15=0

We multiply all the terms by the denominator


2x*x-1*x+15*x-385=0

We add all the numbers together, and all the variables

14x+2x*x-385=0

Wy multiply elements

2x^2+14x-385=0

a = 2; b = 14; c = -385;
Δ = b2-4ac
Δ = 142-4·2·(-385)
Δ = 3276
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:

$\sqrt{\Delta}=\sqrt{3276}=\sqrt{36*91}=\sqrt{36}*\sqrt{91}=6\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{91}}{2*2}=\frac{-14-6\sqrt{91}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{91}}{2*2}=\frac{-14+6\sqrt{91}}{4}
$