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5/8x+1/3x=86
We move all terms to the left:
5/8x+1/3x-(86)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 3x!=0We calculate fractions
x!=0/3
x!=0
x∈R
15x/24x^2+8x/24x^2-86=0
We multiply all the terms by the denominator
15x+8x-86*24x^2=0
We add all the numbers together, and all the variables
23x-86*24x^2=0
Wy multiply elements
-2064x^2+23x=0
a = -2064; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-2064)·0
Δ = 529
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-2064}=\frac{-46}{-4128} =23/2064 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-2064}=\frac{0}{-4128} =0 $
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