5x-6/7x+2=5

Solution for 5x-6/7x+2=5 equation:

5x-6/7x+2=5

We move all terms to the left:

5x-6/7x+2-(5)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

5x-6/7x-3=0

We multiply all the terms by the denominator


5x*7x-3*7x-6=0

Wy multiply elements

35x^2-21x-6=0

a = 35; b = -21; c = -6;
Δ = b2-4ac
Δ = -212-4·35·(-6)
Δ = 1281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{1281}}{2*35}=\frac{21-\sqrt{1281}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1281}}{2*35}=\frac{21+\sqrt{1281}}{70}
$