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3/4x-4=1/2x+6
We move all terms to the left:
3/4x-4-(1/2x+6)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x+6)!=0We get rid of parentheses
x∈R
3/4x-1/2x-6-4=0
We calculate fractions
6x/8x^2+(-4x)/8x^2-6-4=0
We add all the numbers together, and all the variables
6x/8x^2+(-4x)/8x^2-10=0
We multiply all the terms by the denominator
6x+(-4x)-10*8x^2=0
Wy multiply elements
-80x^2+6x+(-4x)=0
We get rid of parentheses
-80x^2+6x-4x=0
We add all the numbers together, and all the variables
-80x^2+2x=0
a = -80; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-80)·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-80}=\frac{-4}{-160} =1/40 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-80}=\frac{0}{-160} =0 $
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