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23=-5x-8/3x
We move all terms to the left:
23-(-5x-8/3x)=0
Domain of the equation: 3x)!=0We get rid of parentheses
x!=0/1
x!=0
x∈R
5x+8/3x+23=0
We multiply all the terms by the denominator
5x*3x+23*3x+8=0
Wy multiply elements
15x^2+69x+8=0
a = 15; b = 69; c = +8;
Δ = b2-4ac
Δ = 692-4·15·8
Δ = 4281
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{-(69)-\sqrt{4281}}{2*15}=\frac{-69-\sqrt{4281}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{4281}}{2*15}=\frac{-69+\sqrt{4281}}{30} $
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