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3/4+2x/4x-24=8/x-6
We move all terms to the left:
3/4+2x/4x-24-(8/x-6)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: x-6)!=0We get rid of parentheses
x∈R
2x/4x-8/x+6-24+3/4=0
We calculate fractions
2x^2/64x^2+(-512x)/64x^2+3x/64x^2+6-24=0
We add all the numbers together, and all the variables
2x^2/64x^2+(-512x)/64x^2+3x/64x^2-18=0
We multiply all the terms by the denominator
2x^2+(-512x)+3x-18*64x^2=0
We add all the numbers together, and all the variables
2x^2+3x+(-512x)-18*64x^2=0
Wy multiply elements
2x^2-1152x^2+3x+(-512x)=0
We get rid of parentheses
2x^2-1152x^2+3x-512x=0
We add all the numbers together, and all the variables
-1150x^2-509x=0
a = -1150; b = -509; c = 0;
Δ = b2-4ac
Δ = -5092-4·(-1150)·0
Δ = 259081
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{259081}=509$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-509)-509}{2*-1150}=\frac{0}{-2300} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-509)+509}{2*-1150}=\frac{1018}{-2300} =-509/1150 $
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