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5/2x-7=3/4x+14=
We move all terms to the left:
5/2x-7-(3/4x+14)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x+14)!=0We get rid of parentheses
x∈R
5/2x-3/4x-14-7=0
We calculate fractions
20x/8x^2+(-6x)/8x^2-14-7=0
We add all the numbers together, and all the variables
20x/8x^2+(-6x)/8x^2-21=0
We multiply all the terms by the denominator
20x+(-6x)-21*8x^2=0
Wy multiply elements
-168x^2+20x+(-6x)=0
We get rid of parentheses
-168x^2+20x-6x=0
We add all the numbers together, and all the variables
-168x^2+14x=0
a = -168; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-168)·0
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-168}=\frac{-28}{-336} =1/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-168}=\frac{0}{-336} =0 $
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