x-7/3x-5=-1

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Solution for x-7/3x-5=-1 equation:



x-7/3x-5=-1
We move all terms to the left:
x-7/3x-5-(-1)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
x-7/3x-4=0
We multiply all the terms by the denominator
x*3x-4*3x-7=0
Wy multiply elements
3x^2-12x-7=0
a = 3; b = -12; c = -7;
Δ = b2-4ac
Δ = -122-4·3·(-7)
Δ = 228
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:
$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{57}}{2*3}=\frac{12-2\sqrt{57}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{57}}{2*3}=\frac{12+2\sqrt{57}}{6} $

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