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x/12x+(5x-12)=3x-8
We move all terms to the left:
x/12x+(5x-12)-(3x-8)=0
Domain of the equation: 12x!=0We get rid of parentheses
x!=0/12
x!=0
x∈R
x/12x+5x-3x-12+8=0
We multiply all the terms by the denominator
x+5x*12x-3x*12x-12*12x+8*12x=0
Wy multiply elements
60x^2-36x^2+x-144x+96x=0
We add all the numbers together, and all the variables
24x^2-47x=0
a = 24; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·24·0
Δ = 2209
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{2209}=47$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*24}=\frac{0}{48} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*24}=\frac{94}{48} =1+23/24 $
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