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8/3x+1/2x=95
We move all terms to the left:
8/3x+1/2x-(95)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x!=0We calculate fractions
x!=0/2
x!=0
x∈R
16x/6x^2+3x/6x^2-95=0
We multiply all the terms by the denominator
16x+3x-95*6x^2=0
We add all the numbers together, and all the variables
19x-95*6x^2=0
Wy multiply elements
-570x^2+19x=0
a = -570; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-570)·0
Δ = 361
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{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-570}=\frac{-38}{-1140} =1/30 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-570}=\frac{0}{-1140} =0 $
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