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3x-3/5x-6=9
We move all terms to the left:
3x-3/5x-6-(9)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
3x-3/5x-15=0
We multiply all the terms by the denominator
3x*5x-15*5x-3=0
Wy multiply elements
15x^2-75x-3=0
a = 15; b = -75; c = -3;
Δ = b2-4ac
Δ = -752-4·15·(-3)
Δ = 5805
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5805}=\sqrt{9*645}=\sqrt{9}*\sqrt{645}=3\sqrt{645}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-3\sqrt{645}}{2*15}=\frac{75-3\sqrt{645}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+3\sqrt{645}}{2*15}=\frac{75+3\sqrt{645}}{30} $
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