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X=3/5X-9
We move all terms to the left:
X-(3/5X-9)=0
Domain of the equation: 5X-9)!=0We get rid of parentheses
X∈R
X-3/5X+9=0
We multiply all the terms by the denominator
X*5X+9*5X-3=0
Wy multiply elements
5X^2+45X-3=0
a = 5; b = 45; c = -3;
Δ = b2-4ac
Δ = 452-4·5·(-3)
Δ = 2085
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{-(45)-\sqrt{2085}}{2*5}=\frac{-45-\sqrt{2085}}{10} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2085}}{2*5}=\frac{-45+\sqrt{2085}}{10} $
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