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2/3x+85/8x+4=14
We move all terms to the left:
2/3x+85/8x+4-(14)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 8x!=0We add all the numbers together, and all the variables
x!=0/8
x!=0
x∈R
2/3x+85/8x-10=0
We calculate fractions
16x/24x^2+255x/24x^2-10=0
We multiply all the terms by the denominator
16x+255x-10*24x^2=0
We add all the numbers together, and all the variables
271x-10*24x^2=0
Wy multiply elements
-240x^2+271x=0
a = -240; b = 271; c = 0;
Δ = b2-4ac
Δ = 2712-4·(-240)·0
Δ = 73441
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{73441}=271$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(271)-271}{2*-240}=\frac{-542}{-480} =1+31/240 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(271)+271}{2*-240}=\frac{0}{-480} =0 $
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