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5x+4/3x+7=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
5x*3x+7*3x+4=0
Wy multiply elements
15x^2+21x+4=0
a = 15; b = 21; c = +4;
Δ = b2-4ac
Δ = 212-4·15·4
Δ = 201
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{-(21)-\sqrt{201}}{2*15}=\frac{-21-\sqrt{201}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{201}}{2*15}=\frac{-21+\sqrt{201}}{30} $
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