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2x-10=39/5x-3
We move all terms to the left:
2x-10-(39/5x-3)=0
Domain of the equation: 5x-3)!=0We get rid of parentheses
x∈R
2x-39/5x+3-10=0
We multiply all the terms by the denominator
2x*5x+3*5x-10*5x-39=0
Wy multiply elements
10x^2+15x-50x-39=0
We add all the numbers together, and all the variables
10x^2-35x-39=0
a = 10; b = -35; c = -39;
Δ = b2-4ac
Δ = -352-4·10·(-39)
Δ = 2785
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{-(-35)-\sqrt{2785}}{2*10}=\frac{35-\sqrt{2785}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{2785}}{2*10}=\frac{35+\sqrt{2785}}{20} $
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