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-41/4x-75/8x=-190
We move all terms to the left:
-41/4x-75/8x-(-190)=0
Domain of the equation: 4x!=0
x!=0/4
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
-41/4x-75/8x+190=0
We calculate fractions
(-328x)/32x^2+(-300x)/32x^2+190=0
We multiply all the terms by the denominator
(-328x)+(-300x)+190*32x^2=0
Wy multiply elements
6080x^2+(-328x)+(-300x)=0
We get rid of parentheses
6080x^2-328x-300x=0
We add all the numbers together, and all the variables
6080x^2-628x=0
a = 6080; b = -628; c = 0;
Δ = b2-4ac
Δ = -6282-4·6080·0
Δ = 394384
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{394384}=628$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-628)-628}{2*6080}=\frac{0}{12160} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-628)+628}{2*6080}=\frac{1256}{12160} =157/1520 $
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