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2x=3/5x+7=0
We move all terms to the left:
2x-(3/5x+7)=0
Domain of the equation: 5x+7)!=0We get rid of parentheses
x∈R
2x-3/5x-7=0
We multiply all the terms by the denominator
2x*5x-7*5x-3=0
Wy multiply elements
10x^2-35x-3=0
a = 10; b = -35; c = -3;
Δ = b2-4ac
Δ = -352-4·10·(-3)
Δ = 1345
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{1345}}{2*10}=\frac{35-\sqrt{1345}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1345}}{2*10}=\frac{35+\sqrt{1345}}{20} $
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