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2x+30x/(2x-6x)=10
We move all terms to the left:
2x+30x/(2x-6x)-(10)=0
Domain of the equation: (2x-6x)!=0We add all the numbers together, and all the variables
x∈R
2x+30x/(-4x)-10=0
We multiply all the terms by the denominator
2x*(-4x)+30x-10*(-4x)=0
We add all the numbers together, and all the variables
30x+2x*(-4x)-10*(-4x)=0
We multiply parentheses
-8x^2+30x+40x=0
We add all the numbers together, and all the variables
-8x^2+70x=0
a = -8; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·(-8)·0
Δ = 4900
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{4900}=70$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70}{2*-8}=\frac{-140}{-16} =8+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-8}=\frac{0}{-16} =0 $
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