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5/6x+7=5/12x
We move all terms to the left:
5/6x+7-(5/12x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 12x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/6x-(+5/12x)+7=0
We get rid of parentheses
5/6x-5/12x+7=0
We calculate fractions
60x/72x^2+(-30x)/72x^2+7=0
We multiply all the terms by the denominator
60x+(-30x)+7*72x^2=0
Wy multiply elements
504x^2+60x+(-30x)=0
We get rid of parentheses
504x^2+60x-30x=0
We add all the numbers together, and all the variables
504x^2+30x=0
a = 504; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·504·0
Δ = 900
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{900}=30$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*504}=\frac{-60}{1008} =-5/84 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*504}=\frac{0}{1008} =0 $
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