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1/7x+3/8x=5
We move all terms to the left:
1/7x+3/8x-(5)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 8x!=0We calculate fractions
x!=0/8
x!=0
x∈R
8x/56x^2+21x/56x^2-5=0
We multiply all the terms by the denominator
8x+21x-5*56x^2=0
We add all the numbers together, and all the variables
29x-5*56x^2=0
Wy multiply elements
-280x^2+29x=0
a = -280; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-280)·0
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-280}=\frac{-58}{-560} =29/280 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-280}=\frac{0}{-560} =0 $
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