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2x-3/5x=11-2
We move all terms to the left:
2x-3/5x-(11-2)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
2x-3/5x-9=0
We multiply all the terms by the denominator
2x*5x-9*5x-3=0
Wy multiply elements
10x^2-45x-3=0
a = 10; b = -45; c = -3;
Δ = b2-4ac
Δ = -452-4·10·(-3)
Δ = 2145
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{2145}}{2*10}=\frac{45-\sqrt{2145}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2145}}{2*10}=\frac{45+\sqrt{2145}}{20} $
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