2x-7=3/x+93

Solution for 2x-7=3/x+93 equation:

2x-7=3/x+93

We move all terms to the left:

2x-7-(3/x+93)=0


Domain of the equation: x+93)!=0

x∈R


We get rid of parentheses

2x-3/x-93-7=0

We multiply all the terms by the denominator


2x*x-93*x-7*x-3=0

We add all the numbers together, and all the variables

-100x+2x*x-3=0

Wy multiply elements

2x^2-100x-3=0

a = 2; b = -100; c = -3;
Δ = b2-4ac
Δ = -1002-4·2·(-3)
Δ = 10024
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:

$\sqrt{\Delta}=\sqrt{10024}=\sqrt{4*2506}=\sqrt{4}*\sqrt{2506}=2\sqrt{2506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2506}}{2*2}=\frac{100-2\sqrt{2506}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2506}}{2*2}=\frac{100+2\sqrt{2506}}{4}
$