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7x-5/3x-5=9
We move all terms to the left:
7x-5/3x-5-(9)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
7x-5/3x-14=0
We multiply all the terms by the denominator
7x*3x-14*3x-5=0
Wy multiply elements
21x^2-42x-5=0
a = 21; b = -42; c = -5;
Δ = b2-4ac
Δ = -422-4·21·(-5)
Δ = 2184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{546}}{2*21}=\frac{42-2\sqrt{546}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{546}}{2*21}=\frac{42+2\sqrt{546}}{42} $
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