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-3/2x-1/4x=7
We move all terms to the left:
-3/2x-1/4x-(7)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x!=0We calculate fractions
x!=0/4
x!=0
x∈R
(-12x)/8x^2+(-2x)/8x^2-7=0
We multiply all the terms by the denominator
(-12x)+(-2x)-7*8x^2=0
Wy multiply elements
-56x^2+(-12x)+(-2x)=0
We get rid of parentheses
-56x^2-12x-2x=0
We add all the numbers together, and all the variables
-56x^2-14x=0
a = -56; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-56)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-56}=\frac{0}{-112} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-56}=\frac{28}{-112} =-1/4 $
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