5x-8/x+7=12/x+7

Solution for 5x-8/x+7=12/x+7 equation:

5x-8/x+7=12/x+7

We move all terms to the left:

5x-8/x+7-(12/x+7)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

5x-8/x-12/x-7+7=0

We multiply all the terms by the denominator


5x*x-7*x+7*x-8-12=0

We add all the numbers together, and all the variables

5x*x-20=0

Wy multiply elements

5x^2-20=0

a = 5; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·5·(-20)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*5}=\frac{20}{10}
=2
$