3/x+7=5x+5

Solution for 3/x+7=5x+5 equation:

3/x+7=5x+5

We move all terms to the left:

3/x+7-(5x+5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3/x-5x-5+7=0

We multiply all the terms by the denominator


-5x*x-5*x+7*x+3=0

We add all the numbers together, and all the variables

2x-5x*x+3=0

Wy multiply elements

-5x^2+2x+3=0

a = -5; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-5)·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*-5}=\frac{6}{-10}
=-3/5
$