5x+5=3/x+7

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

5x+5=3/x+7

We move all terms to the left:

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


Domain of the equation: x+7)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


5x*x-7*x+5*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{-6}{10}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*5}=\frac{10}{10}
=1
$