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

-12x+5x*x-3=0

Wy multiply elements

5x^2-12x-3=0

a = 5; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·5·(-3)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{51}}{2*5}=\frac{12-2\sqrt{51}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{51}}{2*5}=\frac{12+2\sqrt{51}}{10}
$